High-Index High-Dispersion Phosphate Glasses Containing Bismuth Oxide

ABSTRACT

Glass compositions include phosphorus oxide (P 2 O 5 ), niobia (Nb 2 O 5 ), titania (TiO 2 ) and bismuth oxide (Bi 2 O 3 ) as essential components and may optionally include barium oxide (BaO), calcium oxide (CaO), potassium oxide (K 2 O), lithium oxide (Li 2 O), sodium oxide (Na 2 O), tungsten oxide (WO 3 ), boron oxide (B 2 O 3 ) and other components. The glasses may be characterized by high refractive index at 587.56 nm at comparably low density at room temperature.

This Application claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 63/323,648 filed on Mar. 25, 2022, the content of which is relied upon and incorporated herein by reference in its entirety.

FIELD

The present disclosure generally relates to phosphate glasses having a high refractive index and low density. Also, it relates to glasses with high optical dispersion.

BACKGROUND

Glass is used in a variety of optical devices, examples of which include augmented reality devices, virtual reality devices, mixed reality devices, eye wear, etc. Desirable properties for this type of glass often include a high refractive index and a low density. Additional desirable properties may include high transmission in the visible and near-ultraviolet (near-UV) range of the electromagnetic spectrum and/or low optical dispersion. It can be challenging to find glasses having the desired combination of these properties and which can be formed from compositions having good glass-forming ability. For example, generally speaking, as the refractive index of a glass increases, the density also tends to increase. Species such as TiO₂ and Nb2O₅ are often added to increase the refractive index of a glass without increasing the density of the glass. However, these materials often absorb blue and UV light, which can undesirably decrease the transmittance of light in this region of the spectrum by the glass. Often, attempts to increase the refractive index of a glass while maintaining a low density, and without decreasing transmittance in the blue and UV region of the spectrum, can result in a decrease in the glassforming ability of the material. For example, crystallization and/or liquid-liquid phase separation can occur during cooling of the glass melt at cooling rates that are generally acceptable in the industry. Typically, the decrease in glassforming ability appears as the amount of certain species, such as ZrO₂, Y₂O₃, Sc₂O₃, BeO, etc. increases.

Low density, high refractive index glasses often belong to one of two types of chemical systems, based on the glass formers used: (a) silicoborate or borosilicate glasses in which SiO₂ and/or B₂O₃ are used as the main glass formers and (b) phosphate glasses in which P₂O₅ is used as a main glass former. Glasses which rely on other oxides as main glass formers, such as GeO₂, TeO₂, Bi₂O₃, and V₂O₅, can be challenging to use due to cost, glass-forming ability, optical properties, and/or production requirements.

Phosphate glasses can be characterized by a high refractive index and low density, however, phosphate glasses can be challenging to produce due to volatilization of P₂O₅ from the melts and/or risks of platinum incompatibility. In addition, phosphate glasses are often highly colored and may require an extra bleaching step to provide a glass having the desired transmittance characteristic. Furthermore, phosphate glasses exhibiting a high refractive index also tend to have an increase in optical dispersion, which may be usable for some applications.

In view of these considerations, there is a need for phosphate glasses having a high refractive index and low density, optionally in combination with a high transmittance in the visible and near UV-range, and/or which are made from compositions that provide good glass-forming ability.

SUMMARY

According to an embodiment of the present disclosure, a glass comprises a plurality of components, the glass having a composition of the components comprising greater than or equal to 15.9 mol. % and less than or equal to 50.0 mol. % P₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 50.0 mol. % Bi2O₃, greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. % TiO2, greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. % Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.0 mol. % WO₃, greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. % V₂O₅, a sum of TiO₂+Nb₂O₅ greater than or equal to 25.0 mol. % and less than or equal to 70.0 mol. %, a sum of Alk₂O greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, a sum of RO greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, a sum of GeO₂+TeO₂ greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % and may optionally contain Al₂O₃, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥−8.0, where Alk₂O is a total sum of alkali metal oxides, and RO is a total sum of divalent metal oxides.

According to another embodiment of the present disclosure, a glass comprises a plurality of components, the glass having a composition of the components comprising greater than or equal to 23.0 mol. % and less than or equal to 35.0 mol. % P₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 35.0 mol. % Bi₂O₃, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. % Nb₂O₅, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. % TiO₂, greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % Li₂O and may optionally contain one or more components selected from BaO, K₂O, CaO, Na₂O, SrO, WO₃, B₂O₃, SiO₂, ZnO, ZrO₂, MgO, Al₂O₃, TeO₂, PbO, GeO₂, Tl₂O, Ag₂O, CdO, Cs₂O, Ga₂O₃, La₂O₃, MoO₃, Ta₂O₅ and V₂O₅, the glass satisfies the condition: P_(n)−(1.14+0.192*P_(d))>0.000, where P_(n) is a parameter predicting a refractive index at 587.56 nm, n_(d), calculated from the glass composition in terms of mol. % of the components according to the Formula (I):

P _(n)=1.865−0.0052736*P₂O₅+0.0071201*Nb₂O₅+0.0031659*TiO₂−0.0008032*BaO−0.0047736*K₂O−0.00076807*CaO−0.0027991*Na₂O−0.0016514*Li₂O−0.00069646*SrO+0.0032628*WO₃+0.007519*Bi₂O₃−0.0040698*B₂O₃−0.0035951*SiO₂ −0.00067102*ZnO+0.0022313*ZrO₂−0.0019531*MgO−0.003506*Al₂O₃+0.0019216*TeO₂+0.0025766*PbO−0.0018844*GeO₂+0.0065444*Tl₂O+0.0052048*Ag₂O,   (I)

and P_(d) is a parameter predicting a density at room temperature, d_(RT), calculated from the glass composition in terms of mol. % of the components according to the Formula (II):

P _(d)=4.45−0.020780*Al₂O₃−0.020918*B₂O₃+0.014152*BaO+0.061008*Bi₂O₃−0.0067411*CaO+0.013529*CdO+0.012560*Cs₂O+0.0028892*Ga₂O₃−0.0057012*GeO₂−0.017838*K₂O+0.046524*La₂O₃−0.013919*Li₂O−0.010279*MgO−0.0064231*MoO₃−0.012983*Na₂O+0.0083294*Nb₂O₅−0.028926*P₂O₅+0.031742*PbO−0.019022*SiO₂+0.0045214*SrO+0.050158*Ta₂O₅+0.0088486*TeO₂−0.0063053*TiO₂−0.018941*V₂O₅+0.027483*WO₃−0.0010277*ZnO+0.0100487*ZrO₂,   (II).

These and other aspects, objects, and features of the present disclosure will be understood and appreciated by those skilled in the art upon studying the following specification, claims, and appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot illustrating the relationship between the refractive index n_(d) and the refractive index parameter P_(n) calculated by formula (I) for some Comparative Glasses and some Exemplary Glasses according to an embodiment of the present disclosure.

FIG. 2 is a plot illustrating the relationship between the density d_(RT) and the density parameter P_(d) calculated by formula (II) for some Comparative Glasses and some Exemplary Glasses according to an embodiment of the present disclosure.

FIG. 3 is a plot of an exemplary cooling schedule according to a “15 min test” condition and a “2.5 min test” condition for some exemplary glasses according to an embodiment of the present disclosure.

FIG. 4 is a plot illustrating the relationship between the density parameter P_(d) and the refractive index parameter P_(n) for some Comparative Glasses and some Exemplary Glasses according to an embodiment of the present disclosure.

FIG. 5 is a plot illustrating the relationship between the density at room temperature d_(RT) and the refractive index at 587.56 nm n_(d) for some Comparative Glasses and some Exemplary Glasses according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

In the following detailed description, for purposes of explanation and not limitation, example embodiments disclosing specific details are set forth to provide a thorough understanding of various principles of the present disclosure. However, it will be apparent to one having ordinary skill in the art, having had the benefit of the present disclosure, that the present disclosure may be practiced in other embodiments that depart from the specific details disclosed herein. Moreover, descriptions of well-known devices, methods and materials may be omitted so as not to obscure the description of various principles of the present disclosure. Finally, wherever applicable, like reference numerals refer to like elements.

Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not actually recite an order to be followed by its steps, or it is not otherwise specifically stated in the claims or descriptions that the steps are to be limited to a specific order, it is in no way intended that an order be inferred, in any respect. This holds for any possible non-express basis for interpretation, including, without limitation, matters of logic with respect to arrangement of steps or operational flow; plain meaning derived from grammatical organization or punctuation; the number or type of embodiments described in the specification.

As used herein, the term “and/or,” when used in a list of two or more items, means that any one of the listed items can be employed by itself, or any combination of two or more of the listed items can be employed. For example, if a composition is described as containing components A, B, and/or C, the composition can contain A alone; B alone; C alone; A and B in combination; A and C in combination; B and C in combination; or A, B, and C in combination.

Modifications of the disclosure will occur to those skilled in the art and to those who make or use the disclosure. Therefore, it is understood that the embodiments shown in the drawings and described above are merely for illustrative purposes and not intended to limit the scope of the disclosure, which is defined by the following claims, as interpreted according to the principles of patent law, including the doctrine of equivalents.

As used herein, the term “about” means that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and/or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those skilled in the art. When the term “about” is used in describing a value or an end-point of a range, the disclosure should be understood to include the specific value or end-point referred to. Whether or not a numerical value or end-point of a range in the specification recites “about,” the numerical value or end-point of a range is intended to include two embodiments: one modified by “about,” and one not modified by “about.” It will be further understood that the end-points of each of the ranges are significant both in relation to the other end-point, and independently of the other end-point.

The term “component” refers to a material or compound included in a batch composition from which a glass is formed. Components include oxides, including but not limited to those expressed in Formulas (I), and (II), and the claims. Representative components include B₂O₃, P₂O₅, Al₂O₃, CuO, Cu₂O, RO, R₂O, SnO₂, MnO₂, RE_(m)O_(n), SiO₂, Ta₂O₅, ZnO, WO₃, Nb₂O₅, TiO₂, ZrO₂, Bi₂O₃, TeO₂, etc. Other representative components include halogens (e.g. F, Br, CI). Whenever a component is included as a term in a mathematical expression or formula, it is understood that the component refers to the amount of the component in units of mol. % in the batch composition of the glass. For example, the expression “B₂O₃+P₂O₅” refers to the sum of the amount of B₂O₃ in units of mol. % and the amount of P₂O₅ in units of mol. % in the batch composition of the glass. A mathematical expression or formula is any expression or formula that includes a mathematical operator such as “+”, “−”, “*”, “/”, “min”, or “max”.

Unless otherwise specified, the amount or content of a component in a glass composition is expressed herein in units of mol. % (mole percent).

The term “formed from” can mean one or more of comprises, consists essentially of, or consists of. For example, a component that is formed from a particular material can comprise the particular material, consist essentially of the particular material, or consist of the particular material.

The terms “free” and “substantially free” are used interchangeably herein to refer to an amount and/or an absence of a particular component in a glass composition that is not intentionally added to the glass composition. It is understood that the glass composition may contain traces of a particular constituent component as a contaminant or a tramp in an amount of less than 0.10 mol. %.

As used herein, the term “tramp”, when used to describe a particular constituent component in a glass composition, refers to a constituent component that is not intentionally added to the glass composition and is present in an amount of less than 0.10 mol. %. Tramp components may be unintentionally added to the glass composition as an impurity in another constituent component and/or through migration of the tramp component into the composition during processing of the glass composition.

Unless otherwise specified, the term “glass” is used to refer to a glass made from a glass composition disclosed herein.

The symbol “*” means multiplication when used in any formula herein.

Temperature is expressed herein in units of ° C. (degrees Celsius).

Density is expressed herein in units of g/cm³.

Viscosity is expressed herein in units of P (Poise).

The term “glass former” is used herein to refer to a component that, being solely present in the glass composition (i.e., without other components, except for tramps), is able to form a glass when cooling the melt at a rate of not greater than about 300° C./min.

The term “modifier”, as used herein, refers to the oxides of monovalent or divalent metals, i.e., R₂O or RO, where “R” stands for a cation. Modifiers can be added to a glass composition to change the atomic structure of the melt and the resulting glass. In some embodiments, the modifier may change the coordination numbers of cations present in the glass formers (e.g., boron in B₂O₃), which may result in forming a more polymerized atomic network and, as a result, may provide better glass formation.

As used herein, the term “RO” refers to a total content of divalent metal oxides, the term “R₂O” refers to a total content of monovalent metal oxides, and the term “Alk₂O” refers to a total content of alkali metal oxides. The term R₂O encompasses alkali metal oxides (Alk₂O), in addition to other monovalent metal oxides, such as Ag₂O, Tl₂O, and Hg₂O, for example. As discussed below, in the present disclosure, a rare earth metal oxide is referred to herein by its normalized formula (RE₂O₃) in which the rare earth metal has the redox state “+3,” and thus rare earth metal oxides are not encompassed by the term RO.

As used herein, the term “rare earth metals” refers to the metals listed in the Lanthanide Series of the IUPAC Periodic Table, plus yttrium and scandium. As used herein, the term “rare earth metal oxides,” is used to refer to the oxides of rare earth metals in different redox states, such as “+3” for lanthanum in La₂O₃, “+4” for cerium in CeO₂, “+2” for europium in EuO, etc. In general, the redox states of rare earth metals in oxide glasses may vary and, in particular, the redox state may change during melting, based on the batch composition and/or the redox conditions in the furnace where the glass is melted and/or heat-treated (e.g., annealed). Unless otherwise specified, a rare earth metal oxide is referred to herein by its normalized formula in which the rare earth metal has the redox state “+3.” Accordingly, in the case in which a rare earth metal having a redox state other than “+3” is added to the glass composition batch, the glass compositions are recalculated by adding or removing some oxygen to maintain the stoichiometry. For example, when CeO₂ (with cerium in redox state “+4”) is used as a batch component, the resulting glass composition is recalculated assuming that two moles of CeO₂ is equivalent to one mole of Ce₂O₃, and the resulting as-batched glass composition is presented in terms of Ce₂O₃. As used herein, the term “RE_(m)O_(n)” is used to refer to the total content of rare earth metal oxides in all redox states present, and the term “RE₂O₃” is used to refer to the total content of rare earth metal oxides in the “+3” redox state, also specified as “trivalent equivalent”.

Unless otherwise specified, all compositions are expressed in terms of as-batched mole percent (mol %). As will be understood by those having ordinary skill in the art, various melt constituents (e.g., fluorine, alkali metals, boron, etc.) may be subject to different levels of volatilization (e.g., as a function of vapor pressure, melt time and/or melt temperature) during melting of the constituents. As such, the term “about,” in relation to such constituents, is intended to encompass values within about 0.2 mol % when measuring final articles as compared to the as-batched compositions provided herein. With the forgoing in mind, substantial compositional equivalence between final articles and as-batched compositions is expected.

The measured density values for the glasses reported herein were measured at room temperature in units of g/cm³ by Archimedes method in water with an error of 0.001 g/cm³. As used herein, density measurements at room temperature (specified as d_(RT)) are indicated as being measured at 20° C. or 25° C., and encompass measurements obtained at temperatures that may range from 20° C. to 25° C. It is understood that room temperature may vary between about 20° C. to about 25° C., however, for the purposes of the present disclosure, the variation in density within the temperature range of 20° C. to 25° C. is expected to be less than the error of 0.001 g/cm³, and thus is not expected to impact the room temperature density measurements reported herein.

As used herein, good glass forming ability refers to a resistance of the melt to devitrification as the material cools. Glass forming ability can be measured by determining the critical cooling rate of the melt. The terms “critical cooling rate” or “v_(cr)” are used herein to refer to the minimum cooling rate at which a melt of a given composition forms a glass free of crystals visible under an optical microscope under magnification of 500×. The critical cooling rate can be used to measure the glass-forming ability of a composition, i.e., the ability of the melt of a given glass composition to form glass when cooling. Generally speaking, the lower the critical cooling rate, the better the glass-forming ability.

The term “liquidus temperature” (T_(liq)) is used herein to refer to a temperature above which the glass composition is completely liquid with no crystallization of constituent components of the glass. The liquidus temperature values reported herein were obtained by measuring samples using either DSC or by isothermal hold of samples wrapped in platinum foil. For samples measured using DSC, powdered samples were heated at 10 K/min to 1250° C. The end of the endothermal event corresponding to the melting of crystals was taken as the liquidus temperature. For the second technique (isotactic hold), a glass block (about 1 cm³) was wrapped in platinum foil, to avoid volatilization, and placed in a furnace at a given temperature for 17 hours. The glass block was then observed under an optical microscope to check for crystals.

The refractive index values reported herein were measured at room temperature, unless otherwise specified. The refractive index values for a glass sample were measured using a Metricon Model 2010 prism coupler refractometer with an error of about ±0.0002. Using the Metricon, the refractive index of a glass sample was measured at two or more wavelengths of about 406 nm, 473 nm, 532 nm, 633 nm, 828 nm, and 1064 nm. The measured dependence characterizes the dispersion and was then fitted with a Cauchy's law equation or Sellmeier equation to allow for calculation of the refractive index of the sample at a given wavelength of interest between the measured wavelengths. The term “refractive index n_(d)” is used herein to refer to a refractive index calculated as described above at a wavelength of 587.56 nm, which corresponds to the helium d-line wavelength. The term “refractive index n_(C)” is used herein to refer to a refractive index calculated as described above at a wavelength of 656.3 nm. The term “refractive index n_(F)” is used herein to refer to a refractive index calculated as described above at a wavelength of 486.1 nm. The term “refractive index ng” is used herein to refer to a refractive index calculated as described above at a wavelength of 435.8 nm.

As used herein, the terms “high refractive index” or “high index” refers to a refractive index value of a glass that is greater than or equal to at least 1.80, unless otherwise indicated. Where indicated, terms “high refractive index” or “high index” refers to a refractive index value of a glass that is greater than or equal to at least 1.85, greater than or equal to 1.90, or greater than or equal to 1.95, or greater than or equal to 2.00.

The terms “dispersion” and “optical dispersion” are used interchangeably to refer to a difference or ratio of the refractive indices of a glass sample at predetermined wavelengths. One numerical measure of optical dispersion reported herein is the Abbe number, which can be calculated by the formula: v_(x)=(n_(x)−1)/(n_(F)−n_(C)), where “x” in the present disclosure stands for one of the commonly used wavelengths (for example, 587.56 nm [d-line] or 589.3 nm [D-line]), nx is the refractive index at this wavelength, and n_(F) and n_(C) are refractive indices at the wavelengths 486.1 nm (F-line) and 656.3 nm (C-line), respectively. The numerical values of v_(d) and V_(D) differ very slightly, mostly within ±0.1% to ±0.2%. As reported herein, the dispersion of a glass sample is represented by the Abbe number (v_(d)), which characterizes the relationship between the refractive indices of the sample at three different wavelengths according to the following formula: v_(d)=(n_(d)−1)/(n_(F)−n_(C)), where n_(d) is the calculated refractive index at 587.56 nm (d-line), n_(F) is the calculated refractive index at 486.1 nm, and n_(C) is the calculated refractive index at 656.3 nm. A higher Abbe number corresponds to a lower optical dispersion.

The numerical value for an Abbe number corresponding to “high dispersion” or “low dispersion” may vary depending on the refractive indices for which the Abbe number is calculated. In some cases, an Abbe number corresponding to “low dispersion” for a high refractive index glass may be lower than an Abbe number corresponding to “low dispersion” for a low refractive index glass. In other words, as the calculated refractive index value increases, the value of the Abbe number corresponding to low dispersion decreases. The same relates to “high dispersion” as well.

The glass transition temperature (T_(g)) is measured by differential scanning calorimeter (DSC) at the heating rate of 10 K/min after cooling in air.

Glass composition may include phosphorus oxide (P₂O₅). The glass compositions in the embodiments described herein comprise phosphorus oxide (P₂O₅) as a main glass former. Greater amounts of P₂O₅ cause greater viscosity values at a given temperature, which protects the melts from crystallization when cooling and, therefore, improves the glass forming ability of the melt (i.e. lowers the critical cooling rate of the melt). However, P₂O₅ significantly decrease the refractive index. Accordingly, the content of P₂O₅ in high-index glasses is limited. In embodiments, the glass composition may contain phosphorus oxide (P₂O₅) in an amount from greater than or equal to 15.9 mol. % to less than or equal to 50.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain P₂O₅ in an amount greater than or equal to 15.9 mol. %, greater than or equal to 17.5 mol. %, greater than or equal to 18.0 mol. %, greater than or equal to 20.0 mol. %, greater than or equal to 23.0 mol. %, greater than or equal to 23.5 mol. %, greater than or equal to 24.05 mol. %, greater than or equal to 24.5 mol. %, greater than or equal to 35.0 mol. %, greater than or equal to 40.0 mol. %, or greater than or equal to 45.0 mol. %. In some other embodiments, the glass composition may contain P₂O₅ in an amount less than or equal to 50.0 mol. %, less than or equal to 45.0 mol. %, less than or equal to 40.0 mol. %, less than or equal to 35.0 mol. %, less than or equal to 28.0 mol. %, less than or equal to 27.5 mol. %, less than or equal to 25.5 mol. %, less than or equal to 25.0 mol. %, or less than or equal to 20.0 mol. %. In some more embodiments, the glass composition may contain P₂O₅ in an amount greater than or equal to 15.9 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 17.5 mol. % and less than or equal to 27.5 mol. %, greater than or equal to 18.0 mol. % and less than or equal to 28.0 mol. %, greater than or equal to 23.0 mol. % and less than or equal to 35.0 mol. %, greater than or equal to 23.5 mol. % and less than or equal to 25.5 mol. %, greater than or equal to 24.05 mol. % and less than or equal to 25.05 mol. %, greater than or equal to 24.2 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 24.48 mol. % and less than or equal to 24.99 mol. %, greater than or equal to 15.9 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 17.5 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 20.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 23.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 23.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 23.5 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 23.5 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 24.05 mol. % and less than or equal to 25.0 mol. %.

Glass composition may include germania (GeO₂). Germania (GeO₂) provides a high ratio of refractive index to density and does not reduce visible transmittance. Germania is a glass forming oxide. However, germania is expensive and accordingly, the content of germania should be limited, or glass compositions may be free of GeO₂. In embodiments, the glass composition may contain germania (GeO₂) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 25.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain GeO₂ in an amount greater than or equal to 0.0 mol. %, greater than or equal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 19.0 mol. %, greater than or equal to 20.0 mol. %, greater than or equal to 21.0 mol. %, or greater than or equal to 23.0 mol. %. In some other embodiments, the glass composition may contain GeO₂ in an amount less than or equal to 25.0 mol. %, less than or equal to 23.0 mol. %, less than or equal to 21.0 mol. %, less than or equal to 20.0 mol. %, less than or equal to 19.0 mol. %, less than or equal to 10.0 mol. %, or less than or equal to 5.0 mol. %. In some more embodiments, the glass composition may contain GeO₂ in an amount greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 19.0 mol. %, greater than or equal to 19.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 19.0 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 20.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 20.0 mol. % and less than or equal to 21.0 mol. %.

Glass composition may include boron oxide (B₂O₃). According to some embodiments of the present disclosure, boron oxide may play a role of a glass former. As a glass former, B₂O₃ may increase the liquidus viscosity and, therefore, inhibit crystallization. However, adding B₂O₃ to a glass composition may cause liquid-liquid phase separation, which may cause devitrification and/or a reduction in the visible transmittance of the resulting glass. Also, adding B₂O₃ to the high-index glasses reduces the refractive index. Accordingly, the amount of boron oxide is limited, or glasses may be substantially free of B₂O₃. In embodiments, the glass composition may contain boron oxide (B₂O₃) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 10.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain B₂O₃ in an amount greater than or equal to 0.0 mol. %, or greater than or equal to 5.0 mol. %. In some other embodiments, the glass composition may contain B₂O₃ in an amount less than or equal to 10.0 mol. %, less than or equal to 10.0 mol. %, less than or equal to 8.0 mol. %, or less than or equal to 5.0 mol. %. In some more embodiments, the glass composition may contain B₂O₃ in an amount greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 8.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 15.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 8.0 mol. %.

Glass composition may include alkali metal oxides (Alk₂O). Alkali metal oxides (Li₂O, Na₂O, K₂O, Rb₂O and Cs₂O) may help to incorporate high-index components, such as TiO₂, Nb₂O₅ or WO₃, in the glass structure at a given density. Most commonly, Li₂O, Na₂O and/or K₂O are used for this purpose. Among these three oxides, typically, K₂O provides the greatest effect on solubility of the high-index components; however, addition of K₂O itself may reduce the refractive index. Li₂O typically provides the greatest ratio of the refractive index to density among the alkali metal oxides, but it has the lowest effect on solubility of the high-index components. Sodium oxide (Na₂O) typically provides an effect intermediate between Li₂O and K₂O. However, exact effects of these oxides on glass forming ability are difficult to predict, and in different embodiments, the desirable proportions between these oxides may vary. In particular, in some embodiments, it is desirable to add all of three oxides (Li₂O, Na₂O and K₂O), or two of them, together with each other. Also, in some embodiments, use of monovalent metal oxides (R₂O) together with divalent metal oxides (RO) improves the glass forming ability of glasses and may enable higher refractive indices at a given density. Accordingly, in some embodiments of the present disclosure the total content of alkali metal oxides may be limited.

In some embodiments, the glass composition may contain alkali metal oxides Alk₂O in an amount greater than or equal to 0.5 mol. %, greater than or equal to 10.0 mol. %, or greater than or equal to 20.0 mol. %. In some other embodiments, the glass composition may contain alkali metal oxides Alk₂O in an amount less than or equal to 30.0 mol. %, less than or equal to 20.0 mol. %, or less than or equal to 10.0 mol. %. In some more embodiments, the glass composition may contain alkali metal oxides Alk₂O in an amount greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 20.0 mol. %, or greater than or equal to 0.5 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 30.0 mol. %, or greater than or equal to 10.0 mol. % and less than or equal to 20.0 mol. %.

Glass composition may include potassium oxide (K₂O). Potassium oxide may increase the solubility of high-index components, such as TiO₂ and Nb₂O₅, to a degree greater than other monovalent and divalent metal oxides. However, potassium oxide itself provides the lowest refractive index among the alkali metal oxides. Therefore, at high concentrations of K₂O, it may be difficult to reach high refractive index. Accordingly, the amount of K₂O in glasses of the present disclosure is limited, or glasses may be substantially free of K₂O. In embodiments, the glass composition may contain potassium oxide (K₂O) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 25.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain K₂O in an amount greater than or equal to 0.0 mol. %, greater than or equal to 2.0 mol. %, greater than or equal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 19.0 mol. %, greater than or equal to 20.0 mol. %, greater than or equal to 21.0 mol. %, or greater than or equal to 23.0 mol. %. In some other embodiments, the glass composition may contain K₂O in an amount less than or equal to 25.0 mol. %, less than or equal to 23.0 mol. %, less than or equal to 21.0 mol. %, less than or equal to 20.0 mol. %, less than or equal to 19.0 mol. %, less than or equal to 10.0 mol. %, less than or equal to 8.0 mol. %, less than or equal to 7.5 mol. %, or less than or equal to 5.0 mol. %. In some more embodiments, the glass composition may contain K₂O in an amount greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %, greater than or equal to 2.06 mol. % and less than or equal to 7.5 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 7.5 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 19.0 mol. %, greater than or equal to 19.0 mol. % and less than or equal to 20.0 mol. %.

Glass composition may include lithium oxide (Li₂O). Lithium oxide provides the highest ratio of the refractive index to density of glasses among the known monovalent metal oxides. Also, in some embodiments, Li₂O may help to increase the solubility of Nb₂O₅ and TiO₂, which additionally raises the refractive index at a given density. In addition, lithium oxide may hasten the process of bleaching the glasses. However, addition of Li₂O, even in small enough concentrations, may decrease the glass forming ability of glasses, causing crystallization or liquid-liquid phase separation of glassforming melts when cooling. Therefore, the amount of Li₂O is limited. In some embodiments, the glasses may be substantially free of Li₂O. In embodiments, the glass composition may contain lithium oxide (Li₂O) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 25.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain Li₂O in an amount greater than or equal to 0.0 mol. %, greater than or equal to 0.1 mol. %, greater than or equal to 0.3 mol. %, greater than or equal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 19.0 mol. %, greater than or equal to 20.0 mol. %, greater than or equal to 21.0 mol. %, or greater than or equal to 23.0 mol. %. In some other embodiments, the glass composition may contain Li₂O in an amount less than or equal to 25.0 mol. %, less than or equal to 23.0 mol. %, less than or equal to 21.0 mol. %, less than or equal to 20.0 mol. %, less than or equal to 19.0 mol. %, less than or equal to 10.0 mol. %, less than or equal to 7.5 mol. %, less than or equal to 6.5 mol. %, less than or equal to 5.75 mol. %, less than or equal to 5.0 mol. %, or less than or equal to 2.1 mol. %. In some more embodiments, the glass composition may contain Li₂O in an amount greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 5.75 mol. %, greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 0.42 mol. % and less than or equal to 2.08 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 2.1 mol. %, greater than or equal to 0.1 mol. % and less than or equal to 2.1 mol. %, greater than or equal to 0.3 mol. % and less than or equal to 2.1 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 5.75 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 19.0 mol. %, greater than or equal to 19.0 mol. % and less than or equal to 20.0 mol. %.

Glass composition may include sodium oxide (Na₂O). In high-index glasses, Na₂O acts like K₂O, improving the solubility of high-index components, such as TiO₂, Nb₂O₅, WO₃ and others, but, at the same time, Na₂O itself acts to decrease the refractive index of glasses. In most cases, the effect of Na₂O on solubility of high-index components was found to be a little bit lower than the corresponding effect of K₂O. However, Na₂O provides lower thermal expansion coefficient than K₂O, which may reduce the thermal stresses formed when cooling the glass articles and, therefore, improve the quality of the articles. In embodiments, the glass composition may contain sodium oxide (Na₂O) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 20.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain Na₂O in an amount greater than or equal to 0.0 mol. %, greater than or equal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 14.0 mol. %, greater than or equal to 16.0 mol. %, or greater than or equal to 18.0 mol. %. In some other embodiments, the glass composition may contain Na₂O in an amount less than or equal to 20.0 mol. %, less than or equal to 18.0 mol. %, less than or equal to 16.0 mol. %, less than or equal to 14.0 mol. %, less than or equal to 10.0 mol. %, less than or equal to 7.5 mol. %, less than or equal to 6.5 mol. %, less than or equal to 5.75 mol. %, or less than or equal to 5.0 mol. %. In some more embodiments, the glass composition may contain Na₂O in an amount greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 5.75 mol. %, greater than or equal to 0.03 mol. % and less than or equal to 4.97 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. %.

Glass composition may include divalent metal oxides (RO). Divalent metal oxides, such as alkaline earth metal oxides (BeO, MgO, CaO, SrO and BaO), zinc oxide (ZnO), cadmium oxide (CdO), lead oxide (PbO) and others, when present in a glass, provide higher refractive indexes than most monovalent oxides. Some divalent metal oxides, such as, for example, CaO, SrO and ZnO, also provide comparably low density, therefore, increasing the ratio of the refractive index to density and, accordingly, increasing the performance of optical glasses. In addition, divalent metal oxides may help to increase the solubility of the high-index components, such as TiO₂, Nb₂O₅ and WO₃, which leads to a further increase in refractive index at a given density. However, when adding at high amounts, divalent metal oxides may cause crystallization of refractory minerals from the melts or liquid-liquid phase separation, which may reduce the glass-forming ability of glasses. Accordingly, the amount of divalent metal oxides in glass compositions of the present disclosure is limited.

In some embodiments, the glass composition may contain divalent metal oxides RO in an amount greater than or equal to 0.3 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 10.0 mol. %, or greater than or equal to 20.0 mol. %. In some other embodiments, the glass composition may contain divalent metal oxides RO in an amount less than or equal to 30.0 mol. %, less than or equal to 20.0 mol. %, or less than or equal to 10.0 mol. %. In some more embodiments, the glass composition may contain RO in an amount greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, greater than or equal to 0.3 mol. % and less than or equal to 30.0 mol. %, or greater than or equal to 0.3 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 20.0 mol. %, or greater than or equal to 0.5 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 30.0 mol. %, or greater than or equal to 10.0 mol. % and less than or equal to 20.0 mol. %.

Glass composition may include barium oxide (BaO). Barium oxide may increase the solubility of high index components, such as TiO₂ and Nb₂O₅, which leads to an increase the refractive index at a given density. However, barium is a heavy element and, being added in a high amount, may increase the density of glass. Also, in high concentration, it may cause crystallization of minerals such as barium titanate (BaTiO₃), barium niobate (BaNb₂O₆), barium orthophosphate (Ba₃P₂O₈) and others. Accordingly, the amount of BaO in glasses is limited, or glasses may be substantially free of BaO. In embodiments, the glass composition may contain barium oxide (BaO) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 20.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain BaO in an amount greater than or equal to 0.0 mol. %, greater than or equal to 1.75 mol. %, greater than or equal to 3.0 mol. %, or greater than or equal to 10.0 mol. %. In some other embodiments, the glass composition may contain BaO in an amount less than or equal to 20.0 mol. %, less than or equal to 10.0 mol. %, less than or equal to 9.0 mol. %, or less than or equal to 8.0 mol. %. In some more embodiments, the glass composition may contain BaO in an amount greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. %, greater than or equal to 1.75 mol. % and less than or equal to 8.0 mol. %, greater than or equal to 2.59 mol. % and less than or equal to 8.99 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 8.0 mol. %, greater than or equal to 1.75 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 3.0 mol. % and less than or equal to 20.0 mol. %, greater than or equal to 3.0 mol. % and less than or equal to 8.0 mol. %.

Glass composition may include calcium oxide (CaO). Calcium oxide provides the highest ratio of the refractive index to density among the known monovalent and divalent metal oxides. Also, in some embodiments, CaO may help to increase the solubility of Nb₂O₅ and TiO₂, which additionally raises the refractive index at a given density. However, if the amount of CaO in a glass is too high, it may cause crystallization of refractory species, such as calcium titanates (CaTiO₃, CaTi₂O₅, etc.) calcium niobate (CaNb₂O₆), calcium metasilicate (CaSiO₃) and others. This effect may reduce the viscosity at liquidus temperature and, therefore, increase the critical cooling rate, which may cause crystallization of the melt when cooling. The amount of CaO is accordingly limited. In embodiments, the glass composition may contain calcium oxide (CaO) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 17.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain CaO in an amount greater than or equal to 0.0 mol. %, greater than or equal to 1.0 mol. %, or greater than or equal to 10.0 mol. %. In some other embodiments, the glass composition may contain CaO in an amount less than or equal to 17.0 mol. %, less than or equal to 10.0 mol. %, or less than or equal to 9.0 mol. %. In some more embodiments, the glass composition may contain CaO in an amount greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. %, greater than or equal to 0.97 mol. % and less than or equal to 8.99 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 17.0 mol. %, greater than or equal to 1.0 mol. % and less than or equal to 17.0 mol. %, greater than or equal to 1.0 mol. % and less than or equal to 9.0 mol. %.

Glass composition may include vanadia (V₂O₅). Vanadia provides the highest ratio of the refractive index to density among all oxides. However, vanadia may cause undesirable dark or even black coloring and may also raise ecology concerns. For these reasons, the content of vanadia in the glasses is limited, or glass compositions may be free of V₂O₅. In embodiments, the glass composition may contain vanadia (V₂O₅) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 5.0 mol. % and all ranges and sub-ranges between the foregoing values. In some other embodiments, the glass composition may contain V₂O₅ in an amount less than or equal to 5.0 mol. %, less than or equal to 2.5 mol. %, or less than or equal to 1.0 mol. %. In some more embodiments, the glass composition may contain V₂O₅ in an amount greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. %.

Glass composition may include tungsten oxide (WO₃). WO₃ provides high refractive index without significantly increasing density or causing undesirable coloring. However, at high content of WO₃ the liquidus temperature tends to rise and the viscosity at the liquidus temperature drops, making it difficult to avoid crystallization of melts when cooling . Accordingly, the content of tungsten oxide should be limited, or glass compositions may be free of WO₃. In embodiments, the glass composition may contain tungsten oxide (WO₃) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 10.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain WO₃ in an amount greater than or equal to 0.0 mol. %, greater than or equal to 3.93 mol. %, greater than or equal to 5.0 mol. %, greater than or equal to 7.0 mol. %, greater than or equal to 8.0 mol. %, or greater than or equal to 9.0 mol. %. In some other embodiments, the glass composition may contain WO₃ in an amount less than or equal to 10.0 mol. %, less than or equal to 9.0 mol. %, less than or equal to 8.0 mol. %, less than or equal to 7.5 mol. %, less than or equal to 7.0 mol. %, less than or equal to 6.5 mol. %, less than or equal to 6.0 mol. %, less than or equal to 5.0 mol. %, or less than or equal to 4.8 mol. %. In some more embodiments, the glass composition may contain WO₃ in an amount greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 6.0 mol. %, greater than or equal to 3.93 mol. % and less than or equal to 4.8 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 4.8 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 6.0 mol. %, greater than or equal to 8.0 mol. % and less than or equal to 9.0 mol. %.

Glass composition may include bismuth oxide (Bi₂O₃). Bi₂O₃ provides very high refractive index, but leads to an increase in density. However, it may also decrease the viscosity of melts at high temperatures, which may cause crystallization of melts when cooling. This effect is especially significant at high content of Bi₂O₃. Accordingly, the content of bismuth oxide should be limited. In embodiments, the glass composition may contain bismuth oxide (Bi₂O₃) in an amount from greater than or equal to 4.0 mol. % to less than or equal to 50.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain Bi₂O₃ in an amount greater than or equal to 4.0 mol. %, greater than or equal to 4.5 mol. %, greater than or equal to 5.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 25.0 mol. %, greater than or equal to 35.0 mol. %, greater than or equal to 40.0 mol. %, or greater than or equal to 45.0 mol. %. In some other embodiments, the glass composition may contain Bi₂O₃ in an amount less than or equal to 50.0 mol. %, less than or equal to 45.0 mol. %, less than or equal to 40.0 mol. %, less than or equal to 35.0 mol. %, less than or equal to 30.0 mol. %, less than or equal to 25.0 mol. %, less than or equal to 23.0 mol. %, or less than or equal to 10.0 mol. %. In some more embodiments, the glass composition may contain Bi₂O₃ in an amount greater than or equal to 4.0 mol. % and less than or equal to 30.0 mol. %, greater than or equal to 4.5 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 4.5 mol. % and less than or equal to 35.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 30.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 5.0 mol. % and less than or equal to 23.0 mol. %, greater than or equal to 4.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 4.5 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 23.0 mol. %, greater than or equal to 25.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 25.0 mol. % and less than or equal to 30.0 mol. %.

Glass composition may include titania (TiO₂). High refractive index glasses typically include species, such as TiO₂ and Nb₂O₅, that absorb at least a portion of visible light, particularly at blue and near-UV regions wavelengths. In embodiments of the present disclosure, the transmittance of the glass may be characterized for different wavelengths within the range of from about 300 nm to 2300 nm. High transmission in the visible and near-UV range (blue region) is particularly desirable in some applications. High transmittance in the blue can be challenging to achieve in high refractive index glasses. High level of TiO₂ and/or Nb₂O₅ that are typically used in glasses to increase refractive index tend to decrease the transmittance in the near-UV region and shift the UV cut-off to higher wavelengths. Accordingly, the amount of TiO₂ is limited, or the glass compositions may be substantially free from TiO₂. In embodiments, the glass composition may contain titania (TiO₂) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 55.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain TiO₂ in an amount greater than or equal to 0.0 mol. %, greater than or equal to 0.3 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 7.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 13.0 mol. %, greater than or equal to 14.0 mol. %, greater than or equal to 25.0 mol. %, greater than or equal to 40.0 mol. %, greater than or equal to 45.0 mol. %, or greater than or equal to 50.0 mol. %. In some other embodiments, the glass composition may contain TiO₂ in an amount less than or equal to 55.0 mol. %, less than or equal to 50.0 mol. %, less than or equal to 45.0 mol. %, less than or equal to 40.0 mol. %, less than or equal to 36.0 mol. %, less than or equal to 33.0 mol. %, less than or equal to 30.0 mol. %, less than or equal to 25.0 mol. %, or less than or equal to 10.0 mol. %. In some more embodiments, the glass composition may contain TiO₂ in an amount greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 0.3 mol. % and less than or equal to 40.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 7.0 mol. % and less than or equal to 40.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 36.0 mol. %, greater than or equal to 13.0 mol. % and less than or equal to 33.0 mol. %, greater than or equal to 13.7 mol. % and less than or equal to 30.23 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.3 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 7.0 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 7.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 13.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 14.0 mol. % and less than or equal to 25.0 mol. %.

Glass composition may include niobia (Nb₂O₅). Niobia, like titania, can be used to increase the refractive index of glass while also maintaining a low density. However, niobia can introduce a yellow coloring to the glass that cannot be bleached in the same manner as titania, which can result in a loss of transmittance, particularly in the blue and UV range. Niobia, like titania, may cause crystallization and/or phase separation of the melt. In some embodiments, the glasses may be substantially free of Nb₂O₅. In embodiments, the glass composition may contain niobia (Nb₂O₅) in an amount from greater than or equal to 0.0 mol. % to less than or equal to 55.0 mol. % and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass composition may contain Nb₂O₅ in an amount greater than or equal to 0.0 mol. %, greater than or equal to 0.5 mol. %, greater than or equal to 7.0 mol. %, greater than or equal to 10.0 mol. %, greater than or equal to 14.0 mol. %, greater than or equal to 16.5 mol. %, greater than or equal to 19.0 mol. %, greater than or equal to 25.0 mol. %, greater than or equal to 40.0 mol. %, greater than or equal to 45.0 mol. %, or greater than or equal to 50.0 mol. %. In some other embodiments, the glass composition may contain Nb₂O₅ in an amount less than or equal to 55.0 mol. %, less than or equal to 50.0 mol. %, less than or equal to 45.0 mol. %, less than or equal to 40.0 mol. %, less than or equal to 33.0 mol. %, less than or equal to 30.5 mol. %, less than or equal to 29.0 mol. %, less than or equal to 25.0 mol. %, or less than or equal to 10.0 mol. %. In some more embodiments, the glass composition may contain Nb₂O₅ in an amount greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 7.0 mol. % and less than or equal to 40.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 40.0 mol. %, greater than or equal to 14.0 mol. % and less than or equal to 33.0 mol. %, greater than or equal to 16.5 mol. % and less than or equal to 30.5 mol. %, greater than or equal to 18.83 mol. % and less than or equal to 28.82 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 0.5 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 7.0 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 7.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 14.0 mol. % and less than or equal to 55.0 mol. %, greater than or equal to 14.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 16.5 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 19.0 mol. % and less than or equal to 25.0 mol. %.

In some embodiments, the glass composition may have a sum of GeO₂+TeO₂ greater than or equal to 0.0 mol. %, greater than or equal to 10.0 mol. %, or greater than or equal to 20.0 mol. %. In some other embodiments, the glass composition may have a sum of GeO₂+TeO₂ less than or equal to 25.0 mol. %, less than or equal to 20.0 mol. %, or less than or equal to 10.0 mol. %. In some more embodiments, the glass composition may have a sum of GeO₂+TeO₂ greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. %, or greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. %, greater than or equal to 10.0 mol. % and less than or equal to 25.0 mol. %, or greater than or equal to 10.0 mol. % and less than or equal to 20.0 mol. %.

In some embodiments, the glass composition may have a sum of Na₂O+K₂O greater than or equal to 0.0 mol. %, or greater than or equal to 0.3 mol. %.

In some embodiments, the glass composition may have a sum of P₂O₅+B₂O₃ greater than or equal to 0.0 mol. %, or greater than or equal to 20.0 mol. %. In some other embodiments, the glass composition may have a sum of P₂O₅+B₂O₃ less than or equal to 35.0 mol. % or less than or equal to 20.0 mol. %. In some more embodiments, the glass composition may have a sum of P₂O₅+B₂O₃ greater than or equal to 20.0 mol. % and less than or equal to 35.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 35.0 mol. %, or greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. %.

In some embodiments, the glass composition may have a sum of TiO₂+Nb₂O₅ greater than or equal to 0.0 mol. %, greater than or equal to 25.0 mol. %, greater than or equal to 36.0 mol. %, or greater than or equal to 50.0 mol. %. In some other embodiments, the glass composition may have a sum of TiO₂+Nb₂O₅ less than or equal to 70.0 mol. %, less than or equal to 58.0 mol. %, or less than or equal to 50.0 mol. %. In some more embodiments, the glass composition may have a sum of TiO₂+Nb₂O₅ greater than or equal to 25.0 mol. % and less than or equal to 70.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 70.0 mol. %, greater than or equal to 0.0 mol. % and less than or equal to 58.0 mol. %, or greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 25.0 mol. % and less than or equal to 58.0 mol. %, or greater than or equal to 25.0 mol. % and less than or equal to 50.0 mol. %, greater than or equal to 36.0 mol. % and less than or equal to 70.0 mol. %, greater than or equal to 36.0 mol. % and less than or equal to 58.0 mol. %, or greater than or equal to 36.0 mol. % and less than or equal to 50.0 mol. %.

In some embodiments, glass composition may have limitations for a difference Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅. When the difference (Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅) is zero or positive, i.e., the total content of Alk₂O, RO, Bi₂O₃ and triple the content of Al₂O₃ is equal to or greater than the content of P₂O₅ in glass, it is possible to melt the glass from solid materials, such as metaphosphates (KPO₃, NaPO₃, BaP₂O₆, BiPO₄, AlP₃O₉, etc.), which simplifies the melting process and reduces the cost. When the difference (Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅) is negative, it is typically necessary to either use liquid starting materials, such as phosphoric acid (H₃PO₄), which makes the process more complicated and more expensive, or use more expensive solid materials, such as, for example, titanium phosphate (TiP₂O₇), which also increases the cost of starting materials. Accordingly, it is preferable to have the difference (Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅) positive or zero. In some embodiments, the glass may have a difference Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ greater than or equal to −8 mol. %, greater than or equal to 0.000 mol. %, or greater than or equal to 10 mol. %. In some other embodiments, the glass may have a difference Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ less than or equal to 11 mol. %, less than or equal to 10 mol. %, or less than or equal to 0.000 mol. %. In some more embodiments, the glass may have a difference Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ greater than or equal to −8 mol. % and less than or equal to 11 mol. %, greater than or equal to −8 mol. % and less than or equal to 10 mol. %, or greater than or equal to −8 mol. % and less than or equal to 0.000 mol. %, greater than or equal to 0.000 mol. % and less than or equal to 11 mol. %, or greater than or equal to 0.000 mol. % and less than or equal to 10 mol. %.

In some embodiments, the glass may have a refractive index at 587.56 nm n_(d) greater than or equal to 1.8 or greater than or equal to 1.9, or greater than or equal to 2.0.

In some embodiments, the glass may have an Abbe number v_(d) less than or equal to 20.0 or less than or equal to 19.5, or less than or equal to 19.0, or less than or equal to 18.5.

In some embodiments, the glass may have a glass transition temperature T_(g) from greater than or equal to 550° C. to less than or equal to 650° C. and all ranges and sub-ranges between the foregoing values. In some embodiments, the glass may have a glass transition temperature T_(g) greater than or equal to 550° C., greater than or equal to 560° C., greater than or equal to 590° C., greater than or equal to 620° C., greater than or equal to 630° C., or greater than or equal to 640° C. In some other embodiments, the glass may have a glass transition temperature T_(g) less than or equal to 650° C., less than or equal to 640° C., less than or equal to 630° C., less than or equal to 620° C., less than or equal to 590° C., or less than or equal to 560° C. In some more embodiments, the glass may have a glass transition temperature T_(g) greater than or equal to 550° C. and less than or equal to 650° C., greater than or equal to 550° C. and less than or equal to 560° C., greater than or equal to 560° C. and less than or equal to 650° C., greater than or equal to 560° C. and less than or equal to 590° C., greater than or equal to 590° C. and less than or equal to 650° C., greater than or equal to 590° C. and less than or equal to 620° C., greater than or equal to 620° C. and less than or equal to 650° C., greater than or equal to 620° C. and less than or equal to 630° C., greater than or equal to 630° C. and less than or equal to 650° C., greater than or equal to 630° C. and less than or equal to 640° C.

In some embodiments, the glass may have a refractive index to density ratio (“refraction”) (n_(d)−1)/d_(RT) greater than or equal to 0.20 or greater than or equal to 0.22, or greater than or equal to 0.24.

In some embodiments, the glass may have the density at room temperature d_(RT) less than or equal to 5.5 g/cm³, or less than or equal to 5.2 g/cm³ or less than or equal to 5.0 g/cm³, or less than or equal to 4.8 g/cm³, or less than or equal to 4.6 g/cm³, less than or equal to 4.4 g/cm³, or less than or equal to 4.2 g/cm³.

In some embodiments, the glass may have a quantity n_(d)−(1.14+0.192*d_(RT)) greater than or equal to 0.000.

In some embodiments, the glass may have a quantity n_(d)−(1.205+0.192*d_(RT)) greater than or equal to 0.000.

Refractive index n_(d) and density d_(RT) are properties of glass that can be predicted from the glass composition. A linear regression analysis of the Exemplary Glasses of the present disclosure in the EXAMPLES section below and other glass compositions reported in the literature was performed to determine equations that can predict the composition dependences of the refractive index n_(d) and the density d_(RT).

The training dataset of glass compositions satisfying the compositional limitations specified in Table 1 below and having measured values of the properties of interest (n_(d) and d_(RT)), about 100 glass compositions for each property (n_(d) and d_(RT)), were randomly selected from literature data presented in the publicly available SciGlass Information System database and from the Exemplary Glasses from the embodiments presented herein. The linear regression analysis on the above-specified dataset, with the exclusion of outliers, was used to determine the formulas (I) and (II) presented in Table 2 below for predictive parameters P_(n) and P_(d) that predict n_(d) and d_(RT), respectively. Another subset of glass compositions satisfying the compositional limitations of Table 1 was used as a validation set to evaluate the ability to interpolate within the compositional limitations of Table 1 and was used to establish the standard deviations specified in Table 2 for the predictive parameters P_(n) and P_(d). An external dataset of prior art glass compositions, also randomly selected from the SciGlass Information System database, was used to evaluate the ability to predict the properties (n_(d) and d_(RT)) outside of the compositional limits of Table 1 with reasonable accuracy. Multiple iterations of this process were performed in order to determine the best formula for predicting each property (n_(d) and d_(RT)). Formulas (I) and (II) in Table 2 are the result of the analysis.

The data for the Comparative Glass compositions used in the linear regression modeling, including the training dataset, validation dataset and external dataset were obtained from the publically available SciGlass Information System database. Formulas (I) and (II) below were obtained from the linear regression analysis:

P _(n)=1.865−0.0052736*P₂O₅+0.0071201*Nb₂O₅+0.0031659*TiO₂−0.0008032*BaO−0.0047736*K₂O−0.00076807*CaO−0.0027991*Na₂O−0.0016514*Li₂O−0.00069646*SrO+0.0032628*WO₃+0.007519*Bi₂O₃−0.0040698*B₂O₃−0.0035951*SiO₂ −0.00067102*ZnO+0.0022313*ZrO₂−0.0019531*MgO−0.003506*Al₂O₃+0.0019216*TeO₂+0.0025766*PbO−0.0018844*GeO₂+0.0065444*Tl₂O+0.0052048*Ag₂O,   (I)

P _(d)=4.45−0.020780*Al₂O₃−0.020918*B₂O₃+0.014152*BaO+0.061008*Bi₂O₃−0.0067411*CaO+0.013529*CdO+0.012560*Cs₂O+0.0028892*Ga₂O₃−0.0057012*GeO₂−0.017838*K₂O+0.046524*La₂O₃−0.013919*Li₂O−0.010279*MgO−0.0064231*MoO₃−0.012983*Na₂O+0.0083294*Nb₂O₅−0.028926*P₂O₅+0.031742*PbO−0.019022*SiO₂+0.0045214*SrO+0.050158*Ta₂O₅+0.0088486*TeO₂−0.0063053*TiO₂−0.018941*V₂O₅+0.027483*WO₃−0.0010277*ZnO+0.0100487*ZrO₂.   (II)

In Formulas (I) and (II) and Tables 1 and 2, P_(n) is a predictive parameter that predicts the refractive index at 587.56 nm, n_(d), and is calculated from the components of the glass composition expressed in mol. %, and P_(d) is a predictive parameter that predicts the density at room temperature, d_(RT), calculated from the components of the glass composition expressed in mol. %.

In Formulas (I) and (II), each component of the glass composition is listed in terms of its chemical formula, where the chemical formula refers to the concentration of the component expressed in mol. %. For example, for purposes of Formulas (I) and (II), P₂O₅ refers to the concentration of P₂O₅, expressed in mol. %, in the glass composition. It is understood that not all components listed in Formulas (I) and (II) are necessarily present in a particular glass composition and that Formulas (I) and (II) are equally valid for glass compositions that contain less than all of the components listed in the formulas. It is further understood that Formulas (I) and (II) are also valid for glass compositions within the scope and claims of the present disclosure that contain components in addition to the components listed in the formulas. If a component listed in Formulas (I) and (II) is absent in a particular glass composition, the concentration of the component in the glass composition is 0 mol. % and the contribution of the component to the value calculated from the formulas is zero. In Table 1, R_(m)O_(n) is a total sum of all oxides.

TABLE 1 Composition Space Used for Modeling Property n_(d) d_(RT) Min, Max, Min, Max, Component limits mol. % mol. % mol. % mol. % P₂O₅ 10 30 10 30 Nb₂O₅ 5 70 5 70 TiO₂ 5 50 5 50 Bi₂O₃ 1 90 1 90 CaO 0 40 0 40 Na₂O 0 30 0 30 SrO 0 30 0 30 K₂O 0 20 0 20 BaO 0 20 0 20 SiO₂ 0 20 0 20 ZnO 0 20 0 20 B₂O₃ 0 20 0 20 WO₃ 0 15 0 15 Li₂O 0 10 0 10 ZrO₂ 0 10 0 10 MgO 0 10 0 10 R_(m)O_(n) 99 Not limited 99 Not limited TiO₂ + Nb₂O₅ + 40 Not limited 40 Not limited WO₃ + Bi₂O₃ + TeO₂ TiO₂ + Nb₂O₅ + 30 Not limited 30 Not limited Bi₂O₃ P₂O₅ − SiO₂ 10 Not limited 10 Not limited Other species 0 Not limited 0 Not limited

TABLE 2 Property prediction models Predicting Regression Composition Standard Property Abbreviation Unit Parameter Formula Unit Deviation Refractive n_(d) P_(n) Formula (I) Mol. % 0.015 index at 587.56 nm Density at d_(RT) g/cm³ P_(d) Formula (II) Mol. % 0.075 room temperature

FIG. 1 is a plot of the parameter P_(n) calculated by Formula (I) as a function of measured refractive index n_(d) for some Comparative Glasses (“Comp. Glasses”) taken from the literature and some Exemplary Glasses (“Ex. Glasses”). As illustrated by the data in FIG. 1 , the compositional dependence of the parameter P_(n) had a standard deviation within a range of ±0.015 unit of the measured n_(d) for the majority of glasses, which corresponds to the standard error specified in Table 2.

FIG. 2 is a plot of the parameter P_(d) calculated by Formula (II) as a function of measured density d_(RT) for some Literature Glasses (“Comp. Glasses”) and some Exemplary Glasses (“Ex. Glasses”). As illustrated by the data in FIG. 2 , the compositional dependence of the parameter P_(d) had a standard deviation within a range of ±0.075 unit of the measured d_(RT) for the majority of glasses, which corresponds to the standard deviation specified in Table 2.

Table 3 identifies the combination of components and their respective amounts according to some embodiments of the present disclosure. The Exemplary Glasses A in Table 3 may include additional components according to any aspects of the present disclosure as described herein.

TABLE 3 Exemplary Glasses A Component Amount (mol. %) P₂O₅ 15.9 to 50.0 mol. % Bi₂O₃ 4.5 to 50.0 mol. % TiO₂ 0.0 to 50.0 mol. % Nb₂O₅ 0.0 to 50.0 mol. % Li₂O 0.0 to 25.0 mol. % K₂O 0.0 to 25.0 mol. % Na₂O 0.0 to 20.0 mol. % WO₃ 0.0 to 6.0 mol. % Sum of (TiO₂ + Nb₂O₅) 25.0 to 70.0 mol. % Total sum of alkali metal oxides Alk₂O 0.5 to 30.0 mol. % Total sum of divalent metal oxides RO 0.5 to 30.0 mol. % Sum of (GeO₂ + TeO₂) 0.0 to 25.0 mol. %

Exemplary Glasses A according to embodiments of the present disclosure may satisfy the following condition:

Alk₂O+RO+Bi2O₃+3*Al₂O₃−P₂O₅ [mol. %]≥−8.0,

where chemical formulas refer to the amounts of components in glass, expressed in mol. %.

Table 4 identifies the combination of components and their respective amounts according to some embodiments of the present disclosure. The Exemplary Glasses B in Table 4 may include additional components according to any aspects of the present disclosure as described herein.

TABLE 4 Exemplary Glasses B Component Amount (mol. %) P₂O₅ 23.0 to 35.0 mol. % Bi₂O₃ 4.5 to 35.0 mol. % Nb₂O₅ 0.5 to 55.0 mol. % TiO₂ 0.5 to 55.0 mol. % Li₂O 0.3 to 20.0 mol. %

Exemplary Glasses B according to embodiments of the present disclosure may satisfy the following condition:

n _(d)−(1.14+0.192 *d _(RT))>0.000,

where n_(d) is a refractive index at 587.56 nm, and d_(RT) is a density at room temperature.

According to some embodiments of the present disclosure, Exemplary Glasses B may also satisfy the following condition:

n _(d)−(1.205+0.192 *d _(RT))>0.000,

where n_(d) is a refractive index at 587.56 nm, and d_(RT) is a density at room temperature.

EXAMPLES

The following examples describe various features and advantages provided by the disclosure, and are in no way intended to limit the invention and appended claims.

To prepare the glass samples for some exemplary glasses of the present disclosure, about 15 grams of each sample (content of target species was more than 99.99 wt %) was melted from batch raw materials at a temperature of about 1300° C. in platinum or platinum-rhodium crucibles (Pt:Rh=80:20) for 1 hour. One of two controlled cooling conditions were applied. In the first condition (referred to as “15 min test”), it takes about 15 min for the samples to cool from 1100° C. to 500° C. inside a furnace. In the second condition (referred to as “2.5 min test”), it takes about 2.5 min for the samples to cool from 1100° C. to 500° C. Temperature readings were obtained by direct reading of the furnace temperature or using an IR camera reading with calibration scaling. The first condition (15 min test) approximately corresponds to the cooling rate of up to 300 ° C./min at a temperature of 1000° C. and the second test approximately corresponds to the cooling rate of up to 600 ° C./min at 1000° C. The temperature of 1000° C. corresponds approximately to the temperature at which the cooling rate was expected to approach a maximum. When the temperature is lower, the cooling rate also decreases significantly. Typical schedules of the first and second cooling regimes are shown in FIG. 3 . For these samples, in the Table 5, observations referred to as “15-min devit test” and “2.5-min devit test”, are specified; the observation “1” is used to indicate that a glass composition passed a corresponding test, where a composition is deemed to have passed the indicated devit test if a melt of the composition forms a glass free of crystals visible under an optical microscope under magnification from 100× to 500×. The observation “0” is used to denote that a glass composition failed the indicated devit test.

To prepare other glass samples for exemplary glasses of the present disclosure, unless otherwise specified, a one kilogram batch was prepared in a pure platinum crucible. The crucible was placed in a furnace set at a temperature of 1250° C., the temperature in the furnace was then raised to 1300° C. and held at 1300° C. for 2 hours. The furnace temperature was then reduced to 1250° C. and the glass was allowed to equilibrate at this temperature for an hour before being poured on a steel table and annealed at about Tg for an hour.

Some sample melts were also melted in a “one liter” platinum crucible heated by the Joule effect. In this process, approximately 3700 g of raw materials (components as batched) was used. The crucible was filled with the batch components in 1.5 hours at 1250° C. The temperature was then raised to 1300° C. and held for one hour. During this step, the glass was continuously stirred at 60 rpm. The temperature was then decreased to 1200° C. where it was allowed to equilibrate for 30 minutes and the stirring was continued at a rate of 20 rpm. A delivery tube was heated at 1225° C. and the glass melt was casted on a cooled graphite table to form the glass. The glass was formed into a bar of approximately 25 mm in thickness, 50 mm in width, and 90 cm in length. The bars were inspected under an optical microscope to check for crystallization and were all crystal free. The glass quality observed under the optical microscope was good with the bars being striae and bubble free. The glass was placed at about Tg in a lehr oven for 1 hour for a rough annealing. The bars were then annealed in a static furnace for one hour at about Tg and the temperature was then lowered at 1° C./min.

No chemical analysis of the tested samples was performed because chemical analysis was performed for similar samples prepared in independent meltings by XRF (X-ray fluorescence—for all oxides, except for B₂O₃ and Li₂O), by ICP (inductively coupled plasma mass spectrometry—for B₂O₃) and by FES (flame emission spectrometry—for Li₂O). These analyses gave deviations from the batched compositions within ±2.0 mass % for the major components.

Exemplary glass compositions are listed in Table 5. Comparative glass compositions are listed in Table 6. In Tables 5 and 6, the abbreviation “n” with a subscript refers to the refractive index at a corresponding wavelength in nm; for example, n_(632.8 nm) refers to the refractive index at wavelengths of 632.8 nm.

TABLE 5 Exemplary Glass Compositions Exemplary Glass 1 2 3 4 5 6 7 8 Composition-mol. % TiO₂ mol. % 19.99 18.59 17.54 16.46 15.00 25.21 23.01 23.18 Nb₂O₅ mol. % 25.99 27.38 28.44 29.52 30.99 18.65 20.73 15.23 Bi₂O₃ mol. % 5.00 5.00 5.00 5.00 5.00 6.11 6.22 11.54 P₂O₅ mol. % 23.98 23.98 23.98 23.98 23.97 24.49 24.48 24.47 BaO mol. % 8.01 8.00 8.01 8.01 8.01 9.00 9.00 9.00 CaO mol. % 9.01 9.03 9.01 9.02 9.01 8.99 9.00 9.01 K₂O mol. % 8.00 7.99 7.99 7.99 7.99 7.49 7.50 7.50 Na₂O mol. % 0 0 0 0 0 0.0257 0.0263 0.028 SrO mol. % 0 0 0 0 0 0.0153 0.0158 0.0335 Ta₂O₅ mol. % 0.0227 0.0269 0.0272 0.0276 0.028 0.018 0.0185 0.0157 Composition constraints TiO₂ + Nb₂O₅ mol. % 45.98 45.97 45.98 45.98 45.99 43.87 43.74 38.41 Alk₂O + RO + Bi₂O₃ + mol. % 6.038 6.041 6.031 6.047 6.034 7.133 7.275 12.63 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 1.969 d_(RT) g/cm³ 4.095 4.079 4.109 4.123 4.137 4.136 4.148 4.582 n_(632.8 nm) 1.9591 n_(531.9 nm) 1.9858 n_(F (486.13 nm)) 2.0056 ν_(d) 19.1 (n_(d) − 1)/d_(RT) 0.21148 15-min devit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 1.9729 1.9784 1.9827 1.9869 1.9928 1.9444 1.9531 1.9545 P_(d) [for d_(RT)] g/cm³ 4.0629 4.0831 4.099 4.1147 4.1365 4.0442 4.0824 4.3603 P_(n) − (1.14 + 0.192 * P_(d)) 0.0528 0.0544 0.0557 0.0569 0.0586 0.0279 0.0292 −0.0227 P_(n) − (1.205 + 0.192 * P_(d)) −0.0122 −0.0106 −0.0093 −0.0081 −0.0064 −0.0371 −0.0358 −0.0877 Exemplary Glass 9 10 11 12 13 14 15 16 Composition-mol. % TiO₂ mol. % 19.99 19.98 27.84 25.93 22.00 21.99 22.00 22.01 Nb₂O₅ mol. % 23.13 17.18 15.71 11.87 27.01 27.00 27.01 27.01 Bi₂O₃ mol. % 6.86 12.80 6.42 12.17 5.00 5.00 5.00 5.00 P₂O₅ mol. % 24.48 24.48 24.48 24.48 24.84 24.85 24.85 24.85 BaO mol. % 8.99 9.00 9.00 8.99 7.13 7.13 7.13 7.14 CaO mol. % 8.98 8.99 8.99 8.99 7.00 6.99 6.99 6.99 K₂O mol. % 7.50 7.50 7.50 7.50 0 1.89 0 1.77 Li₂O mol. % 0 0 0 0 5.04 5.12 3.56 3.35 Na₂O mol. % 0.0275 0.0294 0.025 0.0274 1.95 0 3.43 1.86 SrO mol. % 0.0164 0.0351 0.0149 0.0328 0 0 0 0 Ta₂O₅ mol. % 0.0231 0.0165 0.014 0.0115 0.0262 0.0263 0.0263 0.0264 Composition constraints TiO₂ + Nb₂O₅ mol. % 43.11 37.16 43.55 37.80 49.01 49.00 49.02 49.02 Alk₂O + RO + Bi₂O₃ + mol. % 7.893 13.87 7.465 13.23 1.283 1.286 1.265 1.254 3 * Al₂O₃ − P₂O₅ Measured properties d_(RT) g/cm³ 4.209 4.629 4.092 4.438 4.124 4.117 4.123 4.107 15-min devit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 1.9654 1.9677 1.9341 1.944 2.0086 2.0049 2.007 2.0033 P_(d) [for d_(RT)] g/cm³ 4.1607 4.4733 4.0218 4.3533 4.0822 4.0729 4.0837 4.0756 P_(n) − (1.14 + 0.192 * P_(d)) 0.0265 −0.0312 0.0219 −0.0318 0.0848 0.0829 0.0829 0.0808 P_(n) − (1.205 + 0.192 * P_(d)) −0.0385 −0.0962 −0.0431 −0.0968 0.0198 0.0179 0.0179 0.0158 Exemplary Glass 17 18 19 20 21 22 23 24 Composition-mol. % TiO₂ mol. % 21.99 21.99 21.99 21.99 22.00 21.99 22.00 22.00 Nb₂O₅ mol. % 27.00 26.99 26.99 27.00 27.00 26.99 27.00 27.00 Bi₂O₃ mol. % 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 P₂O₅ mol. % 24.85 24.83 24.83 24.84 24.85 24.82 24.85 24.84 BaO mol. % 7.13 7.12 7.13 7.13 7.13 7.13 7.13 7.12 CaO mol. % 7.01 7.01 7.00 6.99 7.02 7.03 7.01 6.99 K₂O mol. % 3.35 0 1.79 3.17 4.89 0 1.93 3.43 Li₂O mol. % 3.64 2.06 1.96 1.96 2.08 0 0 0 Na₂O mol. % 0 4.97 3.29 1.89 0 7.01 5.07 3.59 Ta₂O₅ mol. % 0.0265 0.0264 0.0265 0.0266 0.0266 0.0265 0.0266 0.0267 Composition constraints TiO₂ + Nb₂O₅ mol. % 49.00 48.98 48.98 48.99 49.00 48.98 49.01 49.00 Alk₂O + RO + Bi₂O₃ + mol. % 1.278 1.329 1.340 1.300 1.267 1.350 1.275 1.291 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 2.0035 d_(RT) g/cm³ 4.097 4.109 4.122 4.087 4.088 4.120 4.095 4.111 n_(632.8 nm) 1.9924 n_(531.9 nm) 2.0226 n_(F (486.13 nm)) 2.0452 ν_(d) 17.5 (n_(d) − 1)/d_(RT) 0.24493 15-min devit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 2.0003 2.005 2.0013 1.9987 1.9956 2.0027 1.999 1.996 P_(d) [for d_(RT)] g/cm³ 4.0671 4.0845 4.0761 4.0693 4.0612 4.0867 4.0774 4.0699 P_(n) − (1.14 + 0.192 * P_(d)) 0.0794 0.0808 0.0787 0.0774 0.0758 0.0780 0.0762 0.0745 P_(n) − (1.205 + 0.192 * P_(d)) 0.0144 0.0158 0.0137 0.0124 0.0108 0.0130 0.0112 0.0096 Exemplary Glass 25 26 27 28 29 30 31 32 Composition-mol. % TiO₂ mol. % 21.99 22.00 13.92 13.98 11.42 11.18 10.05 10.68 Nb₂O₅ mol. % 26.99 27.00 23.43 23.99 24.31 23.37 25.96 25.06 Bi₂O₃ mol. % 5.00 5.00 24.98 24.99 23.38 23.91 26.01 27.11 P₂O₅ mol. % 24.84 24.84 24.98 24.98 24.66 24.76 25.14 25.08 BaO mol. % 7.13 7.13 4.19 3.99 4.64 3.87 2.59 2.41 CaO mol. % 7.01 7.01 4.21 4.01 2.71 0.96 0.95 0.68 K₂O mol. % 4.95 7.00 4.20 4.01 3.84 4.17 4.56 4.41 WO₃ mol. % 0 0 0 0 4.80 7.32 4.11 3.93 Li₂O mol. % 0 0 0 0 0.16 0.41 0.59 0.60 Na₂O mol. % 2.07 0 0.0384 0 0 0 0 0 SrO mol. % 0 0 0.023 0.0231 0.0466 0.0237 0.0244 0.0246 Ta₂O₅ mol. % 0.0267 0.023 0.0216 0.0217 0.0218 0.0222 0.0229 0.0231 Composition constraints TiO₂ + Nb₂O₅ mol. % 48.98 49.00 37.36 37.97 35.73 34.55 36.02 35.74 Alk₂O + RO + Bi₂O₃ + mol. % 1.320 1.294 12.65 12.04 10.12 8.586 9.580 10.14 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 2.0801 2.0848 d_(RT) g/cm³ 4.065 4.060 5.269 5.272 5.292 5.354 n_(632.8 nm) 2.0681 2.0726 n_(531.9 nm) 2.1006 2.1056 n_(F (486.13 nm)) 2.1250 T_(g) ° C. 568 T_(x) ° C. 702 T_(liq) ° C. 993 ν_(d) 17.4 (n_(d) − 1)/d_(RT) 0.20499 0.20499 15-min devit test (0/1) 1 1 1 1 1 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 1.9929 1.9889 2.1052 2.1108 2.1112 2.1155 2.1326 2.1371 P_(d) [for d_(RT)] g/cm³ 4.0626 4.0526 5.3155 5.3226 5.4035 5.4875 5.5175 5.5713 P_(n) − (1.14 + 0.192 * P_(d)) 0.0729 0.0709 −0.0553 −0.0512 −0.0663 −0.0781 −0.0668 −0.0726 P_(n) − (1.205 + 0.192 * P_(d)) 0.0079 0.0059 −0.1203 −0.1162 −0.1313 −0.1431 −0.1318 −0.1376 Exemplary Glass 33 34 35 36 37 38 39 40 Composition-mol. % TiO₂ mol. % 7.20 25.58 32.49 37.58 25.57 25.56 32.49 32.51 Nb₂O₅ mol. % 28.82 31.96 27.07 23.48 31.96 31.95 27.08 27.08 Bi₂O₃ mol. % 26.01 4.99 4.99 5.00 7.49 9.98 7.49 9.99 P₂O₅ mol. % 25.09 24.97 24.97 24.98 24.98 24.97 24.98 24.97 BaO mol. % 2.56 6.20 5.18 4.44 4.95 3.70 3.94 2.69 CaO mol. % 0.97 0 0 0 0 0 0 0 K₂O mol. % 4.54 4.20 3.18 2.45 2.96 1.70 1.94 0.69 WO₃ mol. % 4.08 0 0 0 0 0 0 0 Li₂O mol. % 0.69 2.03 2.03 1.99 2.00 2.03 2.01 1.99 SrO mol. % 0.0249 0 0 0 0 0 0 0 Al₂O₃ mol. % 0 0.035 0.0495 0.0474 0.055 0.0575 0.0521 0.0546 SiO₂ mol. % 0 0 0 0 0 0.0325 0 0 Ta₂O₅ mol. % 0.0292 0.0283 0.0267 0.0219 0.0296 0.031 0.024 0.0252 Composition constraints TiO₂ + Nb₂O₅ mol. % 36.01 57.54 59.57 61.07 57.54 57.51 59.57 59.59 Alk₂O + RO + Bi₂O₃ + mol. % 9.697 −7.445 −9.443 −10.96 −7.413 −7.389 −9.449 −9.456 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 2.040 2.038 2.036 2.061 2.079 2.059 2.078 d_(RT) g/cm³ 5.355 4.104 4.056 4.011 4.277 4.433 4.228 4.392 T_(g) ° C. 639 634 629 626 614 621 612 T_(x) ° C. 761 782 778 747 739 782 772 (n_(d) − 1)/d_(RT) 0.25341 0.25592 0.25829 0.24807 0.24340 0.25047 0.24545 15-min devit test (0/1) 1 Predicted and calculated properties P_(n) [for n_(d)] 2.1439 2.0509 2.0436 2.0383 2.0766 2.102 2.0694 2.0952 P_(d) [for d_(RT)] g/cm³ 5.5585 4.1224 4.0415 3.9825 4.2794 4.4353 4.1984 4.356 P_(n) − (1.14 + 0.192 * P_(d)) −0.0633 0.1194 0.1276 0.1337 0.1149 0.1105 0.1233 0.1189 P_(n) − (1.205 + 0.192 * P_(d)) −0.1283 0.0544 0.0626 0.0687 0.0499 0.0455 0.0583 0.0539 Exemplary Glass 41 42 43 44 45 46 47 48 Composition-mol. % TiO₂ mol. % 37.58 37.57 21.12 21.11 21.10 34.32 38.72 25.76 Nb₂O₅ mol. % 23.48 23.47 35.18 35.16 35.19 28.61 24.19 32.18 Bi₂O₃ mol. % 7.49 9.99 5.00 7.49 8.50 9.99 9.98 14.98 P₂O₅ mol. % 24.98 24.97 24.99 24.97 24.99 24.97 24.96 24.96 BaO mol. % 3.20 1.95 6.84 5.59 5.09 0 0 0 K₂O mol. % 1.21 0 4.83 3.59 3.09 0 0 0 Li₂O mol. % 1.99 1.97 1.98 2.01 1.98 1.99 2.03 1.99 Al₂O₃ mol. % 0.0499 0.0699 0.0363 0.0379 0.0386 0.0731 0.0698 0.0624 SiO₂ mol. % 0 0 0 0 0 0.031 0.0296 0.0353 Ta₂O₅ mol. % 0.023 0.0202 0.0335 0.0306 0.0312 0.0253 0.0242 0.0288 Composition constraints TiO₂ + Nb₂O₅ mol. % 61.06 61.04 56.29 56.28 56.29 62.92 62.91 57.94 Alk₂O + RO + Bi₂O₃ + mol. % −10.95 −10.85 −6.235 −6.182 −6.219 −12.77 −12.74 −7.806 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 2.059 2.078 2.043 2.096 2.088 2.123 d_(RT) g/cm³ 4.188 4.366 4.146 4.304 4.331 4.359 4.330 4.716 T_(g) ° C. 617 608 642 630 626 609 605 596 T_(x) ° C. 768 750 751 738 735 749 742 712 (n_(d) − 1)/d_(RT) 0.25287 0.24691 0.25157 0.25143 0.25127 0.23813 Predicted and calculated properties P_(n) [for n_(d)] 2.064 2.0894 2.0562 2.0818 2.0922 2.1171 2.0996 2.1531 P_(d) [for d_(RT)] g/cm³ 4.1393 4.2955 4.1759 4.3322 4.3955 4.3304 4.2655 4.7193 P_(n) − (1.14 + 0.192 * P_(d)) 0.1292 0.1247 0.1144 0.1100 0.1082 0.1456 0.1406 0.1070 P_(n) − (1.205 + 0.192 * P_(d)) 0.0642 0.0597 0.0494 0.0450 0.0432 0.0806 0.0756 0.0420 Exemplary Glass 49 50 51 52 53 54 55 56 Composition-mol. % TiO₂ mol. % 21.99 13.51 31.59 35.65 30.23 34.11 23.55 28.88 Nb₂O₅ mol. % 26.99 18.80 26.32 22.28 25.19 21.32 29.43 24.05 Bi₂O₃ mol. % 5.00 24.96 14.98 14.98 17.47 17.47 19.99 19.96 P₂O₅ mol. % 24.85 24.96 24.97 24.96 24.97 24.96 24.99 24.96 BaO mol. % 7.13 5.88 0 0 0 0 0 0 CaO mol. % 7.00 5.88 0 0 0 0 0 0 K₂O mol. % 0 5.87 0 0 0 0 0 0 Li₂O mol. % 7.01 0 2.02 2.01 2.03 2.02 1.97 2.03 Na₂O mol. % 0 0.0744 0 0 0 0 0 0 SrO mol. % 0 0.0445 0 0 0 0 0 0 Al₂O₃ mol. % 0 0 0.0592 0.057 0.0614 0.0593 0.0444 0.0636 SiO₂ mol. % 0 0 0.0335 0.0322 0.0347 0.0335 0 0.036 Ta₂O₅ mol. % 0.0261 0.0157 0.0228 0.0219 0.0236 0.0182 0.0256 0.0245 Composition constraints TiO₂ + Nb₂O₅ mol. % 48.99 32.31 57.92 57.93 55.42 55.43 52.98 52.93 Alk₂O + RO + Bi₂O₃ + mol. % 1.297 17.75 −7.791 −7.802 −5.284 −5.285 −2.901 −2.782 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 2.109 2.101 2.114 2.106 2.133 2.123 d_(RT) g/cm³ 4.699 4.685 4.842 4.822 5.020 5.010 T_(g) ° C. 594 589 581 582 581 577 T_(x) ° C. 740 731 729 721 721 718 (n_(d) − 1)/d_(RT) 0.23601 0.23501 0.23007 0.22937 0.22570 0.22415 Predicted and calculated properties P_(n) [for n_(d)] 2.0107 2.0602 2.1297 2.1139 2.1361 2.1209 2.1642 2.1424 P_(d) [for d_(RT)] g/cm³ 4.0799 5.2612 4.6328 4.5739 4.784 4.7274 5.0161 4.9352 P_(n) − (1.14 + 0.192 * P_(d)) 0.0874 −0.0900 0.1002 0.0957 0.0775 0.0732 0.0611 0.0549 P_(n) − (1.205 + 0.192 * P_(d)) 0.0224 −0.1550 0.0352 0.0307 0.0125 0.0082 −0.0039 −0.0101 Exemplary Glass 57 58 59 60 61 62 63 64 Composition-mol. % TiO₂ mol. % 32.58 23.65 19.97 12.98 19.81 12.83 10.96 20.01 Nb₂O₅ mol. % 20.35 7.36 10.44 12.98 13.61 23.14 24.56 18.83 Bi₂O₃ mol. % 19.97 18.94 19.53 24.97 24.97 24.97 27.92 24.99 P₂O₅ mol. % 24.95 24.47 24.47 24.96 24.97 24.97 25.04 24.97 BaO mol. % 0 8.99 8.99 7.99 5.51 3.44 2.29 3.71 CaO mol. % 0 8.99 8.99 8.00 5.51 1.74 0.50 3.72 K₂O mol. % 0 7.50 7.49 7.98 5.51 4.27 4.28 3.70 WO₃ mol. % 0 0 0 0 0 4.27 3.80 0 Li₂O mol. % 2.03 0 0 0 0 0.33 0.60 0 Na₂O mol. % 0 0.0605 0.0631 0.0713 0.0712 0 0 0.037 SrO mol. % 0 0.0362 0.0377 0.064 0.0426 0.0235 0.0248 0.0221 Al₂O₃ mol. % 0.0616 0 0 0 0 0 0 0 SiO₂ mol. % 0.0348 0 0 0 0 0 0 0 Ta₂O₅ mol. % 0.019 0.0085 0.0088 0.01 0.015 0.0221 0.0232 0.0156 Composition constraints TiO₂ + Nb₂O₅ mol. % 52.93 31.01 30.41 25.96 33.41 35.96 35.52 38.84 Alk₂O + RO + Bi₂O₃ + mol. % −2.767 20.05 20.64 24.11 16.64 9.801 10.58 11.20 3 * Al₂O₃ − P₂O₅ Measured properties n_(d) 2.113 d_(RT) g/cm³ 5.004 5.269 T_(g) ° C. 572 553 T_(x) ° C. 702 658 T_(liq) ° C. 986 (n_(d) − 1)/d_(RT) 0.22242 15-min devit test (0/1) 1 1 Predicted and calculated properties P_(n) [for n_(d)] 2.1279 1.9555 1.9703 2.0037 2.0455 2.1153 2.1412 2.095 P_(d) [for d_(RT)] g/cm³ 4.8814 4.7425 4.8276 5.194 5.1824 5.4378 5.6147 5.2446 P_(n) − (1.14 + 0.192 * P_(d)) 0.0507 −0.0951 −0.0966 −0.1335 −0.0895 −0.0687 −0.0768 −0.0520 P_(n) − (1.205 + 0.192 * P_(d)) −0.0143 −0.1601 −0.1616 −0.1985 −0.1545 −0.1337 −0.1418 −0.1170 Exemplary Glass 65 66 67 68 69 70 71 72 Composition-mol. % TiO₂ mol. % 24.65 14.38 20.53 24.66 29.24 15.27 16.15 13.70 Nb₂O₅ mol. % 14.05 28.25 22.98 19.13 14.47 22.72 21.85 22.31 Bi₂O₃ mol. % 25.00 24.98 24.98 24.99 24.99 26.58 27.67 26.03 P₂O₅ mol. % 24.99 24.97 24.97 24.98 24.99 25.31 25.54 25.18 BaO mol. % 3.75 2.44 2.16 2.06 2.08 2.72 1.85 2.62 CaO mol. % 3.74 2.46 2.15 2.04 2.08 2.72 1.83 0.97 K₂O mol. % 3.75 2.43 2.15 2.07 2.08 4.48 4.81 4.60 WO₃ mol. % 0 0 0 0 0 0 0 4.15 Li₂O mol. % 0 0 0 0 0 0.16 0.25 0.41 Na₂O mol. % 0.0356 0.0397 0.0381 0.0369 0.0355 0 0 0 SrO mol. % 0.0213 0.0237 0.0228 0.0221 0.0213 0.0234 0.0236 0.0237 Ta₂O₅ mol. % 0.015 0.0278 0.0214 0.0155 0.015 0.0219 0.0222 0.0223 Composition constraints TiO₂ + Nb₂O₅ mol. % 38.70 42.64 43.52 43.79 43.71 37.98 38.00 36.01 Alk₂O + RO + Bi₂O₃ + mol. % 11.29 7.391 6.523 6.227 6.302 11.37 10.90 9.457 3 * Al₂O₃ − P₂O₅ Measured properties d_(RT) g/cm³ 5.278 5.266 5.271 5.278 5.365 5.365 5.376 T_(g) ° C. 555 T_(x) ° C. 681 T_(liq) ° C. 1004 973 15-min devit test (0/1) 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 2.0753 2.1522 2.136 2.1222 2.1034 2.1155 2.1189 2.1182 P_(d) [for d_(RT)] g/cm³ 5.1751 5.3717 5.2918 5.2346 5.1666 5.3714 5.4057 5.4669 P_(n) − (1.14 + 0.192 * P_(d)) −0.0583 −0.0191 −0.0200 −0.0228 −0.0286 −0.0558 −0.0590 −0.0714 P_(n) − (1.205 + 0.192 * P_(d)) −0.1233 −0.0841 −0.0850 −0.0878 −0.0936 −0.1208 −0.1240 −0.1364 Exemplary Glass 73 74 75 76 77 78 Composition-mol. % TiO₂ mol. % 13.70 14.08 20.82 7.36 9.94 13.37 Nb₂O₅ mol. % 22.31 21.66 34.44 29.27 28.28 27.01 Bi₂O₃ mol. % 26.03 27.19 8.32 4.81 4.89 5.00 P₂O₅ mol. % 25.18 25.14 24.31 17.89 19.40 21.41 BaO mol. % 2.62 2.44 5.05 19.07 19.61 20.34 CaO mol. % 0.97 0.67 0.24 0 0 0 K₂O mol. % 4.60 4.41 3.19 4.67 3.41 1.74 WO₃ mol. % 4.15 3.96 0 0 0 0 Li₂O mol. % 0.41 0.42 3.56 0 0 0 Na₂O mol. % 0 0 0 5.92 5.64 5.21 B₂O₃ mol. % 0 0 0 6.55 6.27 5.83 GeO₂ mol. % 0 0 0 4.33 2.46 0 SrO mol. % 0.0237 0.024 0 0.10 0.0856 0.0681 Al₂O₃ mol. % 0 0 0.038 0 0 0 Ta₂O₅ mol. % 0.0223 0.0225 0.0307 0.0282 0.0281 0.024 Composition constraints TiO₂ + Nb₂O₅ mol. % 36.01 35.74 55.26 36.63 38.22 40.38 Alk₂O + RO + Bi₂O₃ + mol. % 9.457 10.00 −3.845 16.68 14.23 10.95 3 * Al₂O₃ − P₂O₅ GeO₂ + TeO₂ mol. % 0 0 0 4.325 2.458 0 Measured properties n_(d) 2.0932 d_(RT) g/cm³ 5.370 5.438 n_(632.8 nm) 2.0808 n_(531.9 nm) 2.1143 (n_(d) − 1)/d_(RT) 0.20358 15-min devit test (0/1) 1 1 1 2.5-min devit test (0/1) 1 1 1 Predicted and calculated properties P_(n) [for n_(d)] 2.1182 2.1243 2.085 1.9494 1.9543 1.9614 P_(d) [for d_(RT)] g/cm³ 5.4669 5.5284 4.3739 4.3732 4.3603 4.3453 P_(n) − (1.14 + 0.192 * P_(d)) −0.0714 −0.0772 0.1052 −0.0302 −0.0229 −0.0129 P_(n) − (1.205 + 0.192 * P_(d)) −0.1364 −0.1422 0.0402 −0.0952 −0.0879 −0.0779

Table 6 below lists the glass compositions and properties for Comparative Glasses C1-C12.

TABLE 6 Compositions and Properties of Comparative Example Glasses Comparative Examples C1 C2 C3 C4 Reference [2] [3] [1] [6] Composition-mol. % P₂O₅ mol. % 31.11 25.50 25.50 23.51 Bi₂O₃ mol. % 5.49 23.99 23.99 17.11 ZnO mol. % 14.28 0 0 0 Na₂O mol. % 15.00 10.51 10.51 2.77 Al₂O₃ mol. % 7.98 0 0 0 K₂O mol. % 7.40 1.99 1.99 0 Li₂O mol. % 15.55 2.02 2.02 2.60 Nb₂O₅ mol. % 1.75 17.99 17.99 18.72 TiO₂ mol. % 1.46 7.00 7.00 21.38 WO₃ mol. % 0 8.00 8.00 7.49 BaO mol. % 0 1.00 1.00 0 B₂O₃ mol. % 0 2.00 2.00 6.43 SiO₂ mol. % 0 0 0 0 Measured properties n_(d) 1.6332 2.0339 2.0702 d_(RT) g/cm³ 5.320 4.990 n_(632.8 nm) 1.6299 2.0230 2.0582 n_(531.9 nm) 1.6385 2.0525 2.0907 n_(F (486.13 nm)) 1.6444 2.0743 2.1149 T_(g) ° C. 350.40 497.00 540.20 T_(liq) ° C. 930.00 1010.0 ν_(d) 39.9 18.5 17.3 (n_(d) − 1)/d_(RT) 0.19434 0.21447 Predicted and calculated properties P_(n) [for n_(d)] 1.619 2.036 2.036 2.057 P_(d) [for d_(RT)] g/cm³ 3.167 5.274 5.274 4.834 Comparative Examples C5 C6 C7 C8 Reference [7] [4] [5] [8] Composition-mol. % P₂O₅ mol. % 23.51 25.42 22.98 25.71 Bi₂O₃ mol. % 17.11 23.93 21.49 20.56 ZnO mol. % 0 0 0 0 Na₂O mol. % 2.77 10.45 6.81 7.37 Al₂O₃ mol. % 0 0 0 0 K₂O mol. % 0 1.97 2.10 1.74 Li₂O mol. % 2.60 2.32 8.23 7.79 Nb₂O₅ mol. % 18.72 17.93 17.29 17.90 TiO₂ mol. % 21.38 6.95 7.08 7.39 WO₃ mol. % 7.49 7.98 8.30 7.37 BaO mol. % 0 1.06 1.80 1.48 B₂O₃ mol. % 6.43 1.99 3.00 2.69 SiO₂ mol. % 0 0 0.91 0 Measured properties n_(d) 2.0702 2.0339 2.000 d_(RT) g/cm³ 4.990 5.100 5.100 n_(632.8 nm) 2.0582 2.0230 1.9897 n_(531.9 nm) 2.0907 2.0525 2.0175 n_(F (486.13 nm)) 2.1149 2.0743 2.0380 T_(g) ° C. 540.20 483.00 479.00 T_(liq) ° C. 1010.0 ν_(d) 17.3 18.5 19.0 (n_(d) − 1)/d_(RT) 0.21447 0.19608 Predicted and calculated properties P_(n) [for n_(d)] 2.057 2.035 2.018 2.005 P_(d) [for d_(RT)] g/cm³ 4.834 5.270 5.128 4.995 Comparative Examples C9 C10 C11 C12 Reference [10] [9] [11] [12] Composition-mol. % P₂O₅ mol. % 24.00 25.69 25.32 24.00 Bi₂O₃ mol. % 5.00 20.57 4.70 8.00 Na₂O mol. % 14.99 7.38 0 11.00 K₂O mol. % 2.00 1.74 1.91 1.99 Li₂O mol. % 20.02 7.80 16.38 17.99 Nb₂O₅ mol. % 18.00 17.91 23.27 19.00 TiO₂ mol. % 5.00 7.34 0.71 6.01 WO₃ mol. % 5.00 7.32 10.78 6.00 BaO mol. % 2.00 1.48 4.60 2.00 B₂O₃ mol. % 4.01 2.70 0 4.01 Sb₂O₃ mol. % 0 0.0814 0.0604 0 GeO₂ mol. % 0 0 10.00 0 Cs₂O mol. % 0 0 2.26 0 MoO₃ mol. % 0 0 0.0122 0 Measured properties n_(d) 1.8442 2.000 1.9055 1.9002 d_(RT) g/cm³ 3.885 5.100 4.271 4.194 n_(632.8 nm) 1.8370 1.8971 1.8919 n_(531.9 nm) 1.8563 1.9194 1.9141 n_(F (486.13)) 1.8702 1.9357 1.9302 T_(g) ° C. 449.00 479.00 521.00 461.00 T_(liq) ° C. 910.00 900.00 ν_(d) 23.3 21.7 21.5 (n_(d) − 1)/d_(RT) 0.21730 0.19608 0.21200 0.21463 Predicted and calculated properties P_(n) [for n_(d)] 1.834 2.005 1.911 1.884 P_(d) [for d_(RT)] g/cm³ 3.752 4.995 4.264 4.045

The reference key for each of the Comparative Glasses listed in Table 6 is as follows: [1] CN113024107A; [2] JP2004123448A; [3] JP2006111499A; [4] JP2010083701; [5] US2021179479; [6] US8647994B2; [7] US8716157B2; [8] W02019151404A1; [9] US2021048665; [10] US7309670B2; [11] US7553785B2; [12] US7994082B2.

FIG. 4 is a plot showing the relationship between the density parameter P_(d) and the refractive index parameter P_(n) for some of the Exemplary Glasses and some of the Comparative Glasses. The Exemplary Glasses (filled circles) are the Examples 13 to 21, 34 to 49, 51 to 57 and 75 from Table 5. The Comparative Glasses (open circles) are the Examples C1 to C8 from Table 6. The refractive index parameter P_(n) that predicts refractive index at 587.56 nm n_(d) was determined according to Formula (I). The density parameter P_(d) that predicts density at room temperature d_(RT) was determined according to Formula (II). All of the Exemplary Glasses and Comparative Glasses shown in FIG. 4 have the features specified in Table 7.

TABLE 7 Limitations for glass compositions shown in FIGS. 4 and 5 Component Unit Min Max P₂O₅ mol. % 23 35 Bi₂O₃ mol. % 4.5 35 Nb₂O₅ mol. % 0.5 55 TiO₂ mol. % 0.5 55 Li₂O mol. % 0.3 20

The Comparative Glasses of FIG. 4 were selected as having the highest value of the parameter P_(n) over the range of values of the parameter P_(d) shown in FIG. 4 among the known glasses that have the features specified in Table 7.

The line corresponding to the formula y=1.14+0.192*x shown in FIG. 4 provides a visual representation of the differences between the Comparative Glasses having the features specified in Table 7 and the Exemplary Glasses 13 to 21, 34 to 49, 51 to 57 and 75. As can be seen in FIG. 4 , the mentioned Exemplary Glasses (filled circles) and none of the Comparative Glasses (open circles) represented in FIG. 4 fall above the line y=1.14+0.192*x , where y corresponds to the parameter P_(n) that predicts refractive index at 587.56 nm and x corresponds to the parameter P_(d) that predicts density at room temperature. In other words, some of the Exemplary Glasses and none of the Comparative Glasses represented in FIG. 4 satisfy the following formula (III)(a):

P _(n)−(1.14+0.192*P _(d))>0.00 (III)(a)

As can also be seen in FIG. 4 , some of Exemplary Glasses and none of the Comparative Glasses represented in FIG. 4 fall above the line y=1.18+0.192*x, where y corresponds to the parameter P_(n) that predicts refractive index at 587.56 nm and x corresponds to the parameter P_(d) that predicts density at room temperature. In other words, some of the Exemplary Glasses and none of the Comparative Glasses represented in FIG. 4 satisfy the following formula (III)(b):

P _(n)−(1.18+0.192*P _(d))>0.00 (III)(b)

The Exemplary Examples represented in FIG. 4 are, by prediction, superior in terms of the combination of d_(RT) and n_(d) (i.e. lower d_(RT) for a given n_(d) or higher n_(d) for a given d_(RT)) to the best known Comparative Glasses that have the features specified in Table 7.

FIG. 5 is a plot showing the relationship between the density at room temperature d_(RT) and the refractive index at 587.56 nm n_(d) for some of the Exemplary Glasses and some of the Comparative Glasses. The Exemplary Glasses (filled circles) are the Examples 17, 34 to 43, 46 to 48 and 51 to 57 from Table 5. The Comparative Glasses (open circles) are the Examples C2, C4, C5, C7 and C9 to C12 from Table 6. All of the Exemplary Glasses and Comparative Glasses shown in FIG. 5 have the features specified in Table 7.

The Comparative Glasses shown in FIG. 5 were selected as having the highest measured values of the refractive index at 587.56 nm n_(d) over the range of values of the density at room temperature d_(RT) shown in FIG. 5 among the known glasses that have the mentioned features specified in Table 7.

The line corresponding to the formula y=1.140+0.192*x shown in FIG. 5 provides a visual representation of the differences between the Comparative Glasses having the features specified in Table 7 and the Exemplary Glasses 17, 34 to 43, 46 to 48 and 51 to 57. As can be seen in FIG. 5 , the mentioned Exemplary Glasses (filled circles) and none of the Comparative Glasses (open circles) represented in FIG. 5 fall above the line y=1.140+0.192*x, where y corresponds to n_(d) and x corresponds to d_(RT). In other words, some of the Exemplary Glasses and none of the Comparative Glasses represented in FIG. 5 satisfy the following formula (IV)(a):

n _(d)−(1.140+0.192*d _(RT))>0.00 (IV)(a)

As can also be seen in FIG. 5 , some of Exemplary Glasses and none of the Comparative Glasses represented in FIG. 5 fall above the line y=1.18+0.192*x, where y corresponds to n_(d) and x corresponds to d_(RT). In other words, some of the Exemplary Glasses and none of the Comparative Glasses represented in FIG. 5 satisfy the following formula (IV)(b):

n _(d)−(1.18+0.192*d _(RT))>0.00 (IV)(b)

The Exemplary Examples represented in FIG. 5 that satisfy the formula (IV)(b) are characterized by the highest values of n_(d) at comparable values of d_(RT) among the glasses that have the features specified in Table 7.

This means that, under the conditions specified in Table 7 above, some of the Exemplary Glasses have higher measured values of the refractive index at 587.56 nm n_(d) at comparable measured values of the density at room temperature d_(RT) than the best of the Comparative Glasses satisfying the same conditions. This can be interpreted as these Exemplary Glasses, according to measurements, have higher values of n_(d) at comparable values of d_(RT) among the said glasses, i.e. they are, according to measurement, superior in terms of combination of d_(RT) and n_(d) (i.e. lower d_(RT) for a given n_(d) or higher n_(d) for a given d_(RT)) to the best known Comparative Glasses that have the features specified in Table 7.

The values of all attributes specified in Table 7 and Formulas (III)(a), (III)(b), (IV)(a) and (IV)(b) for the Comparative Glasses C1 to C12 plotted in FIGS. 4 and 5 are presented in Table 8 below. Full compositions of the Comparative Glasses are presented in Table 6. Full compositions and attributes of the Exemplary Glasses are presented in Table 5.

TABLE 8 Attributes of Comparative Example Glasses Having the Features Specified in Table 7 Ex. # C1 C2 C3 C4 C5 C6 Composition Bi₂O₃ mol. % 5.49 24.00 19.90 17.11 17.11 23.93 Nb₂O₅ mol. % 1.75 18.00 26.87 18.72 18.72 17.93 TiO₂ mol. % 1.45 7.00 4.40 21.39 21.39 6.95 Li₂O mol. % 15.55 2.00 3.92 2.57 2.57 2.32 Measured properties d_(RT) g/cm³ 5.320 4.990 4.990 n_(d) 2.0339 2.0702 2.0702 n_(d) − (1.14 + 0.192 * d_(RT)) −0.1275 −0.0279 −0.0279 n_(d) − (1.18 + 0.192 * d_(RT)) −0.1675 −0.0679 −0.0679 Predicted and calculated properties P_(d) g/cm³ 3.1667 5.2747 5.1594 4.8343 4.8343 5.2695 P_(n) 1.6187 2.0362 2.0765 2.0569 2.0569 2.0351 P_(n) − (1.14 + 0.192 * P_(d)) −0.1293 −0.1165 −0.0541 −0.0113 −0.0113 −0.1166 P_(n) − (1.18 + 0.192 * P_(d)) −0.1693 −0.1565 −0.0941 −0.0513 −0.0513 −0.1566 Ex. # C7 C8 C9 C10 C11 C12 Composition Bi₂O₃ mol. % 21.50 20.57 5.00 20.59 4.70 8.00 Nb₂O₅ mol. % 17.30 17.91 18.00 17.92 23.27 19.00 TiO₂ mol. % 7.10 7.38 5.00 7.33 0.71 6.00 Li₂O mol. % 8.20 7.80 20.00 7.80 16.38 18.00 Measured properties d_(RT) g/cm³ 5.100 3.885 5.100 4.271 4.194 n_(d) 2.000 1.8442 2.000 1.9055 1.9002 n_(d) − (1.14 + 0.192 * d_(RT)) −0.1192 −0.0417 −0.1192 −0.0546 −0.0451 n_(d) − (1.18 + 0.192 * d_(RT)) −0.1592 −0.0817 −0.1592 −0.0946 −0.0851 Predicted and calculated properties P_(d) g/cm³ 5.1295 4.9964 3.7522 4.996 4.2644 4.0447 P_(n) 2.0186 2.0052 1.8339 2.005 1.9112 1.8845 P_(n) − (1.14 + 0.192 * P_(d)) −0.1063 −0.0941 −0.0266 −0.0942 −0.0476 −0.0321 P_(n) − (1.18 + 0.192 * P_(d)) −0.1463 −0.1341 −0.0666 −0.1342 −0.0876 −0.0721

As follows from FIGS. 4 and 5 , both predicted and measured property data confirms that some of the Exemplary Glasses have a better combination of refractive index at 587.56 nm n_(d) and density at room temperature d_(RT) than the best of the Comparative Glasses that have the features specified in Table 7.

The following non-limiting aspects are encompassed by the present disclosure. To the extent not already described, any one of the features of the first through the thirty-fifth aspect may be combined in part or in whole with features of any one or more of the other aspects of the present disclosure to form additional aspects, even if such a combination is not explicitly described.

According to a first aspect, the glass comprises a plurality of components, the glass having a composition of the components comprising greater than or equal to 15.9 mol. % and less than or equal to 50.0 mol. % P₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 50.0 mol. % Bi₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. % Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.0 mol. % WO₃, greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. % V₂O₅, a sum of TiO₂+Nb₂O₅ greater than or equal to 25.0 mol. % and less than or equal to 70.0 mol. %, a sum of Alk₂O greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, a sum of RO greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, a sum of GeO₂+TeO₂ greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % and may optionally contain Al₂O₃, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥−8.0, where Alk₂O is a total sum of alkali metal oxides, and RO is a total sum of divalent metal oxides.

According to a second aspect, the glass of the first aspect, wherein the glass satisfies the conditions: P_(d)<4.8 and P_(n)>2.0, where P_(n) is a parameter predicting a refractive index at 587.56 nm, n_(d), calculated from the glass composition in terms of mol. % of the components according to the Formula (I):

P _(n)=1.865−0.0052736*P₂O₅+0.0071201*Nb₂O₅+0.0031659*TiO₂−0.0008032*BaO−0.0047736*K₂O−0.00076807*CaO−0.0027991*Na₂O−0.0016514*Li₂O−0.00069646*SrO+0.0032628*WO₃+0.007519*Bi₂O₃−0.0040698*B₂O₃−0.0035951*SiO₂ −0.00067102*ZnO+0.0022313*ZrO₂−0.0019531*MgO−0.003506*Al₂O₃+0.0019216*TeO₂+0.0025766*PbO−0.0018844*GeO₂+0.0065444*Tl₂O+0.0052048*Ag₂O,   (I)

and P_(d) is a parameter predicting a density at room temperature, d_(RT), calculated from the glass composition in terms of mol. % of the components according to the Formula (II):

P _(d)=4.45−0.020780*Al₂O₃−0.020918*B₂O₃+0.014152*BaO+0.061008*Bi₂O₃−0.0067411*CaO+0.013529*CdO+0.012560*Cs₂O+0.0028892*Ga₂O₃−0.0057012*GeO₂−0.017838*K₂O+0.046524*La₂O₃−0.013919*Li₂O−0.010279*MgO−0.0064231*MoO₃−0.012983*Na₂O+0.0083294*Nb₂O₅−0.028926*P₂O₅+0.031742*PbO−0.019022*SiO₂+0.0045214*SrO+0.050158*Ta₂O₅+0.0088486*TeO₂−0.0063053*TiO₂−0.018941*V₂O₅+0.027483*WO₃−0.0010277*ZnO+0.0100487*ZrO₂,   (II).

According to a third aspect, the glass of any one of aspects 1-2, wherein the glass has a density at room temperature, d_(RT), that is less than or equal to 4.8 and a refractive index at 587.56 nm, n_(d), that is greater than or equal to 2.0.

According to a fourth aspect, the glass of any one of aspects 1-3, wherein the glass has an Abbe number, v_(d), that is less than or equal to 20.

According to a fifth aspect, the glass of the fourth aspect, wherein the Abbe number, v_(d), is less than or equal to 18.5.

According to a sixth aspect, the glass of any one of aspects 1-5, wherein the glass has a glass transition temperature, T_(g), that is greater than or equal to 550° C. and less than or equal to 650° C.

According to a seventh aspect, the glass of any one of aspects 1-6, wherein when cooled in air from 1100° C. to 500° C. in 15 minutes, the glass does not crystallize.

According to an eighth aspect, the glass of any one of aspects 1-7, wherein the composition of the components comprises greater than or equal to 23.5 mol. % and less than or equal to 25.5 mol. % P₂O₅, greater than or equal to 10.0 mol. % and less than or equal to 40.0 mol. % Nb₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 30.0 mol. % Bi₂O₃, greater than or equal to 0.3 mol. % and less than or equal to 40.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % Li₂O and greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O.

According to a ninth aspect, the glass of any one of aspects 1-8, wherein the composition of the components comprises one or more of the following components: greater than or equal to 24.05 mol. % and less than or equal to 25.05 mol. % P₂O₅, greater than or equal to 14.0 mol. % and less than or equal to 33.0 mol. % Nb₂O₅, greater than or equal to 10.0 mol. % and less than or equal to 36.0 mol. % TiO₂, greater than or equal to 5.0 mol. % and less than or equal to 25.0 mol. % Bi₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. % Li₂O and greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. % Na₂O.

According to a tenth aspect, the glass of any one of aspects 1-9, wherein the composition of the components comprises greater than or equal to 24.2 mol. % and less than or equal to 25.0 mol. % P₂O₅, greater than or equal to 16.5 mol. % and less than or equal to 30.5 mol. % Nb₂O₅, greater than or equal to 13.0 mol. % and less than or equal to 33.0 mol. % TiO₂, greater than or equal to 5.0 mol. % and less than or equal to 23.0 mol. % Bi₂O₃, greater than or equal to 1.75 mol. % and less than or equal to 8.00 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. % K₂O, greater than or equal to 0 mol. % and less than or equal to 5.75 mol. % Li₂O and greater than or equal to 0 mol. % and less than or equal to 5.75 mol. % Na₂O.

According to an eleventh aspect, the glass of any one of aspects 1-10, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥0.000.

According to a twelfth aspect, the glass of any one of aspects 1-7 and 11, wherein the composition of the components comprises greater than or equal to 18.0 mol. % and less than or equal to 28.0 mol. % P₂O₅, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % TeO₂, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. % GeO₂, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. % SiO₂ and a sum of P₂O₅+B₂O₃ greater than or equal to 20.0 mol. % and less than or equal to 35.0 mol. %.

According to a thirteenth aspect, the glass of any one of aspects 1-12, wherein the composition of the components comprises greater than or equal to 0.1 mol. % Li₂O and a sum of Na₂O+K₂O greater than or equal to 0.3 mol. %.

According to a fourteenth aspect, the glass of any one of aspects 1-13, wherein the composition of the components comprises greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % R₂O and greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % RO, where R₂O is a total sum of monovalent metal oxides.

According to a fifteenth aspect, a method for manufacturing an optical element, the method comprising processing a glass, wherein the glass is the glass of any one of aspects 1-14.

According to a sixteenth aspect, an optical element comprising glass, wherein the glass is the glass of any one of aspects 1-15.

According to a seventeenth aspect, the glass comprises a plurality of components, the glass having a composition of the components comprising greater than or equal to 23.0 mol. % and less than or equal to 35.0 mol. % P₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 35.0 mol. % Bi₂O₃, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. % Nb₂O₅, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. % TiO₂, greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % Li₂O and may optionally contain one or more components selected from BaO, K₂O, CaO, Na₂O, SrO, WO₃, B₂O₃, SiO₂, ZnO, ZrO₂, MgO, Al₂O₃, TeO₂, PbO, GeO₂, Tl₂O, Ag₂O, CdO, Cs₂O, Ga₂O₃, La₂O₃, MoO₃, Ta₂O₅ and V₂O₅, the glass satisfies the condition: P_(n)−(1.14+0.192 *P_(d))>0.000, where P_(n) is a parameter predicting a refractive index at 587.56 nm, n_(d), calculated from the glass composition in terms of mol. % of the components according to the Formula (I):

P _(n)=1.865−0.0052736*P₂O₅+0.0071201*Nb₂O₅+0.0031659*TiO₂−0.0008032*BaO−0.0047736*K₂O−0.00076807*CaO−0.0027991*Na₂O−0.0016514*Li₂O−0.00069646*SrO+0.0032628*WO₃+0.007519*Bi₂O₃−0.0040698*B₂O₃−0.0035951*SiO₂ −0.00067102*ZnO+0.0022313*ZrO₂−0.0019531*MgO−0.003506*Al₂O₃+0.0019216*TeO₂+0.0025766*PbO−0.0018844*GeO₂+0.0065444*Tl₂O+0.0052048*Ag₂O,   (I)

and P_(d) is a parameter predicting a density at room temperature, d_(RT), calculated from the glass composition in terms of mol. % of the components according to the Formula (II):

P _(d)=4.45−0.020780*Al₂O₃−0.020918*B₂O₃+0.014152*BaO+0.061008*Bi₂O₃−0.0067411*CaO+0.013529*CdO+0.012560*Cs₂O+0.0028892*Ga₂O₃−0.0057012*GeO₂−0.017838*K₂O+0.046524*La₂O₃−0.013919*Li₂O−0.010279*MgO−0.0064231*MoO₃−0.012983*Na₂O+0.0083294*Nb₂O₅−0.028926*P₂O₅+0.031742*PbO−0.019022*SiO₂+0.0045214*SrO+0.050158*Ta₂O₅+0.0088486*TeO₂−0.0063053*TiO₂−0.018941*V₂O₅+0.027483*WO₃−0.0010277*ZnO+0.0100487*ZrO₂,   (II).

According to an eighteenth aspect, the glass of the seventeenth aspect, wherein the glass satisfies the condition: n_(d)−(1.14+0.192*d_(RT))>0.000, where n_(d) is a refractive index at 587.56 nm and d_(RT) [g/cm³] is a density at room temperature.

According to a nineteenth aspect, the glass of any one of aspects 17-18, wherein the glass satisfies the condition: n_(d)−(1.205+0.192*d_(RT))>0.000, where n_(d) is a refractive index at 587.56 nm and d_(RT) [g/cm³] is a density at room temperature.

According to a twentieth aspect, the glass of any one of aspects 17-19, wherein the glass satisfies the condition: P_(n)−(1.205+0.192*P_(d))>0.000.

According to a twenty-first aspect, the glass of any one of aspects 17-20, wherein the glass satisfies the conditions: P_(d)<4.8 and P_(n)>2.0.

According to a twenty-second aspect, the glass of any one of aspects 17-21, wherein the glass has a density at room temperature, d_(RT), that is less than or equal to 4.8 g/cm³ and a refractive index at 587.56 nm, n_(d), that is greater than or equal to 2.0.

According to a twenty-third aspect, the glass of any one of aspects 17-22, wherein the glass has an Abbe number, v_(d), that is less than or equal to 20.

According to a twenty-fourth aspect, the glass of the twenty-third aspect, wherein the Abbe number, v_(d), is less than or equal to 18.5.

According to a twenty-fifth aspect, the glass of any one of aspects 17-24, wherein the glass has a glass transition temperature, T_(g) that is greater than or equal to 550° C. and less than or equal to 650° C.

According to a twenty-sixth aspect, the glass of any one of aspects 17-25, wherein when cooled in air from 1100° C. to 500° C. in 15 minutes, the glass does not crystallize.

According to a twenty-seventh aspect, the glass of any one of aspects 17-26, wherein the composition of the components comprises greater than or equal to 23.5 mol. % and less than or equal to 25.5 mol. % P₂O₅, greater than or equal to 10.0 mol. % and less than or equal to 40.0 mol. % Nb₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 30.0 mol. % Bi₂O₃, greater than or equal to 0.5 mol. % and less than or equal to 40.0 mol. % TiO₂, greater than or equal to 0.3 mol. % and less than or equal to 10.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O and greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % WO₃.

According to a twenty-eighth aspect, the glass of any one of aspects 17-27, wherein the composition of the components comprises one or more of the following components: greater than or equal to 24.05 mol. % and less than or equal to 25.05 mol. % P₂O₅, greater than or equal to 14.0 mol. % and less than or equal to 33.0 mol. % Nb₂O₅, greater than or equal to 10.0 mol. % and less than or equal to 36.0 mol. % TiO₂, greater than or equal to 5.0 mol. % and less than or equal to 25.0 mol. % Bi₂O₃, greater than or equal to 0.3 mol. % and less than or equal to 6.5 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. % Na₂O and greater than or equal to 0.0 mol. % and less than or equal to 6.5 mol. % WO₃.

According to a twenty-ninth aspect, the glass of any one of aspects 17-28, wherein the composition of the components comprises greater than or equal to 24.2 mol. % and less than or equal to 25.0 mol. % P₂O₅, greater than or equal to 16.5 mol. % and less than or equal to 30.5 mol. % Nb₂O₅, greater than or equal to 13.0 mol. % and less than or equal to 33.0 mol. % TiO₂, greater than or equal to 5.0 mol. % and less than or equal to 23.0 mol. % Bi₂O₃, greater than or equal to 1.75 mol. % and less than or equal to 8.00 mol. % BaO, greater than or equal to 0.3 mol. % and less than or equal to 5.8 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.0 mol. % WO₃ and greater than or equal to 0 mol. % and less than or equal to 5.75 mol. % Na₂O.

According to a thirtieth aspect, the glass of any one of aspects 17-29, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥0.000, where Alk₂O is a total sum of alkali metal oxides, and RO is a total sum of divalent metal oxides.

According to a thirty-first aspect, the glass of any one of aspects 17-26 and 30, wherein the composition of the components comprises greater than or equal to 23.0 mol. % and less than or equal to 28.0 mol. % P₂O₅, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % TeO₂, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. % GeO₂, greater than or equal to 0.0 mol. % and less than or equal to 5.0 mol. % SiO₂ and a sum of P₂O₅+B₂O₃ greater than or equal to 20.0 mol. % and less than or equal to 35.0 mol. %.

According to a thirty-second aspect, the glass of any one of aspects 17-31, wherein the composition of the components comprises a sum of Na₂O+K₂O greater than or equal to 0.3 mol. %.

According to a thirty-third aspect, the glass of any one of aspects 17-32, wherein the composition of the components comprises greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % R₂O and greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % RO, where R₂O is a total sum of monovalent metal oxides, and RO is a total sum of divalent metal oxides.

According to a thirty-fourth aspect, a method for manufacturing an optical element, the method comprising processing a glass, wherein the glass is the glass of any one of aspects 17-33.

According to a thirty-fifth aspect, an optical element comprising glass, wherein the glass is the glass of any one of aspects 17-34.

Many variations and modifications may be made to the above-described embodiments of the disclosure without departing substantially from the spirit and various principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

To the extent not already described, the different features of the various aspects of the present disclosure may be used in combination with each other as desired. That a particular feature is not explicitly illustrated or described with respect to each aspect of the present disclosure is not meant to be construed that it cannot be, but it is done for the sake of brevity and conciseness of the description. Thus, the various features of the different aspects may be mixed and matched as desired to form new aspects, whether or not the new aspects are expressly disclosed. 

1. A glass comprising a plurality of components, the glass having a composition of the components comprising: greater than or equal to 15.9 mol. % and less than or equal to 50.0 mol. % P₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 50.0 mol. % Bi₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and less than or equal to 50.0 mol. % Nb₂O₅, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 20.0 mol. % Na₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.0 mol. % WO₃, greater than or equal to 0.0 mol. % and less than or equal to 1.0 mol. % V₂O₅, a sum of TiO₂+Nb₂O₅ greater than or equal to 25.0 mol. % and less than or equal to 70.0 mol. %, a sum of Alk₂O greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, a sum of RO greater than or equal to 0.5 mol. % and less than or equal to 30.0 mol. %, a sum of GeO₂+TeO₂ greater than or equal to 0.0 mol. % and less than or equal to 25.0 mol. % and optionally comprising Al₂O₃, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥−8.0. where Alk₂O is a total sum of alkali metal oxides and RO is a total sum of divalent metal oxides.
 2. The glass of claim 1, wherein the glass satisfies the conditions: P_(d)<4.8 and P_(b)>2.0, where P_(n) is a parameter predicting a refractive index at 587.56 nm, n_(d), calculated from the glass composition in terms of mol. % of the components according to the Formula (I): P _(n)=1.865−0.0052736*P₂O₅+0.0071201*Nb₂O₅+0.0031659*TiO₂−0.0008032*BaO−0.0047736*K₂O−0.00076807*CaO−0.0027991*Na₂O−0.0016514*Li₂O−0.00069646*SrO+0.0032628*WO₃+0.007519*Bi₂O₃−0.0040698*B₂O₃−0.0035951*SiO₂ −0.00067102*ZnO+0.0022313*ZrO₂−0.0019531*MgO−0.003506*Al₂O₃+0.0019216*TeO₂+0.0025766*PbO−0.0018844*GeO₂+0.0065444*Tl₂O+0.0052048*Ag₂O,   (I) and P_(d) is a parameter predicting a density at room temperature, d_(RT), calculated from the glass composition in terms of mol. % of the components according to the Formula (II): P _(d)=4.45−0.020780*Al₂O₃−0.020918*B₂O₃+0.014152*BaO+0.061008*Bi₂O₃−0.0067411*CaO+0.013529*CdO+0.012560*Cs₂O+0.0028892*Ga₂O₃−0.0057012*GeO₂−0.017838*K₂O+0.046524*La₂O₃−0.013919*Li₂O−0.010279*MgO−0.0064231*MoO₃−0.012983*Na₂O+0.0083294*Nb₂O₅−0.028926*P₂O₅+0.031742*PbO−0.019022*SiO₂+0.0045214*SrO+0.050158*Ta₂O₅+0.0088486*TeO₂−0.0063053*TiO₂−0.018941*V₂O₅+0.027483*WO₃−0.0010277*ZnO+0.0100487*ZrO₂,   (II).
 3. The glass of claim 1, wherein the glass has an Abbe number, v_(d), that is less than or equal to
 20. 4. The glass of claim 1, wherein when cooled in air from 1100° C. to 500° C. in 15 minutes, the glass does not crystallize.
 5. The glass of claim 1, wherein the composition of the components comprises: greater than or equal to 23.5 mol. % and less than or equal to 25.5 mol. % P₂O₅, greater than or equal to 10.0 mol. % and less than or equal to 40.0 mol. % Nb₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 30.0 mol. % Bi₂O₃, greater than or equal to 0.3 mol. % and less than or equal to 40.0 mol. % TiO₂, greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % Li₂O and greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O.
 6. The glass of claim 1, wherein the composition of the components comprises: greater than or equal to 24.2 mol. % and less than or equal to 25.0 mol. % P₂O₅, greater than or equal to 16.5 mol. % and less than or equal to 30.5 mol. % Nb₂O₅, greater than or equal to 13.0 mol. % and less than or equal to 33.0 mol. % TiO₂, greater than or equal to 5.0 mol. % and less than or equal to 23.0 mol. % Bi₂O₃, greater than or equal to 1.75 mol. % and less than or equal to 8.00 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. % K₂O, greater than or equal to 0 mol. % and less than or equal to 5.75 mol. % Li₂O and greater than or equal to 0 mol. % and less than or equal to 5.75 mol. % Na₂O.
 7. The glass of claim 1, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥0.000.
 8. The glass of claim 1, wherein the composition of the components comprises: greater than or equal to 0.1 mol. % Li₂O and a sum of Na₂O+K₂O is greater than or equal to 0.3 mol. %.
 9. A method for manufacturing an optical element, the method comprising processing a glass, wherein the glass is the glass of claim
 1. 10. An optical element comprising glass, wherein the glass is the glass of claim
 1. 11. A glass comprising a plurality of components, the glass having a composition of the components comprising: greater than or equal to 23.0 mol. % and less than or equal to 35.0 mol. % P₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 35.0 mol. % Bi₂O₃, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. % Nb₂O₅, greater than or equal to 0.5 mol. % and less than or equal to 55.0 mol. % TiO₂, greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % Li₂O and optionally comprising one or more components selected from BaO, K₂O, CaO, Na₂O, SrO, WO₃, B₂O₃, SiO₂, ZnO, ZrO₂, MgO, Al₂O₃, TeO₂, PbO, GeO₂, Tl₂O, Ag₂O, CdO, Cs₂O, Ga₂O₃, La₂O₃, MoO₃, Ta₂O5 and V₂O₅, wherein the glass satisfies the condition: P_(n)(1.14+0.192*P_(d))>0.000, where P_(n) is a refractive index at 587.56 nm, n_(d), calculated from the glass composition in terms of mol. % of the components according to the Formula (I): P _(n)=1.865−0.0052736*P₂O₅+0.0071201*Nb₂O₅+0.0031659*TiO₂−0.0008032*BaO−0.0047736*K₂O−0.00076807*CaO−0.0027991*Na₂O−0.0016514*Li₂O−0.00069646*SrO+0.0032628*WO₃+0.007519*Bi₂O₃−0.0040698*B₂O₃−0.0035951*SiO₂ −0.00067102*ZnO+0.0022313*ZrO₂−0.0019531*MgO−0.003506*Al₂O₃+0.0019216*TeO₂+0.0025766*PbO−0.0018844*GeO₂+0.0065444*Tl₂O+0.0052048*Ag₂O,   (I) and P_(d) is a parameter predicting a density at room temperature, d_(RT), calculated from the glass composition in terms of mol. % of the components according to the Formula (II): P _(d)=4.45−0.020780*Al₂O₃−0.020918*B₂O₃+0.014152*BaO+0.061008*Bi₂O₃−0.0067411*CaO+0.013529*CdO+0.012560*Cs₂O+0.0028892*Ga₂O₃−0.0057012*GeO₂−0.017838*K₂O+0.046524*La₂O₃−0.013919*Li₂O−0.010279*MgO−0.0064231*MoO₃−0.012983*Na₂O+0.0083294*Nb₂O₅−0.028926*P₂O₅+0.031742*PbO−0.019022*SiO₂+0.0045214*SrO+0.050158*Ta₂O₅+0.0088486*TeO₂−0.0063053*TiO₂−0.018941*V₂O₅+0.027483*WO₃−0.0010277*ZnO+0.0100487*ZrO₂,   (II).
 12. The glass of claim 11, wherein the glass satisfies the condition: n_(d)−(1.14+0.192*d_(RT))>0.000, where n_(d) is a refractive index at 587.56 nm, d_(RT) [g/cm³] is a density at room temperature.
 13. The glass of claim 11, wherein the glass has an Abbe number, v_(d), that is less than or equal to
 20. 14. The glass of claim 11, wherein when cooled in air from 1100° C. to 500° C. in 15 minutes, the glass does not crystallize.
 15. The glass of claim 11, wherein the composition of the components comprises: greater than or equal to 23.5 mol. % and less than or equal to 25.5 mol. % P₂O₅, greater than or equal to 10.0 mol. % and less than or equal to 40.0 mol. % Nb₂O₅, greater than or equal to 4.5 mol. % and less than or equal to 30.0 mol. % Bi₂O₃, greater than or equal to 0.5 mol. % and less than or equal to 40.0 mol. % TiO₂, greater than or equal to 0.3 mol. % and less than or equal to 10.0 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 15.0 mol. % B₂O₃, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % BaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % Na₂O and greater than or equal to 0.0 mol. % and less than or equal to 10.0 mol. % WO₃.
 16. The glass of claim 11, wherein the composition of the components comprises: greater than or equal to 24.2 mol. % and less than or equal to 25.0 mol. % P₂O₅, greater than or equal to 16.5 mol. % and less than or equal to 30.5 mol. % Nb₂O₅, greater than or equal to 13.0 mol. % and less than or equal to 33.0 mol. % TiO₂, greater than or equal to 5.0 mol. % and less than or equal to 23.0 mol. % Bi₂O₃, greater than or equal to 1.75 mol. % and less than or equal to 8.00 mol. % BaO, greater than or equal to 0.3 mol. % and less than or equal to 5.8 mol. % Li₂O, greater than or equal to 0.0 mol. % and less than or equal to 9.0 mol. % CaO, greater than or equal to 0.0 mol. % and less than or equal to 7.5 mol. % K₂O, greater than or equal to 0.0 mol. % and less than or equal to 6.0 mol. % WO₃ and greater than or equal to 0 mol. % and less than or equal to 5.75 mol. % Na₂O.
 17. The glass of claim 11, wherein the composition of the components satisfies the condition: Alk₂O+RO+Bi₂O₃+3*Al₂O₃−P₂O₅ [mol. %]≥0.000, where chemical formulas mean the content of corresponding components in the glass, Alk₂O is a total sum of alkali metal oxides and RO is a total sum of divalent metal oxides.
 18. The glass of claim 11, wherein the composition comprises: a sum of Na₂O+K₂O is greater than or equal to 0.3 mol. %.
 19. The glass of claim 11, wherein the composition of the components comprises: greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % R₂O and greater than or equal to 0.3 mol. % and less than or equal to 20.0 mol. % RO, where R₂O is a total sum of monovalent metal oxides and RO is a total sum of divalent metal oxides.
 20. An optical element comprising glass, wherein the glass is the glass of claim
 11. 